A  Practical  Course  in 
Mechanical  Drawing 

For  Individual  Study  and  Shop  Classes, 
Trade  and  High  Schools 


BY 

WILLIAM  F.WILLARD 

FORMERLY  INSTRUCTOR  IN  MECHANICAL  DRAWING  AT  THE 
ARMOUR    INSTITUTE  OF  TECHNOLOGY 


With  157  Illustrations,  a  Reference  Vocabulary 
and  Definitions  of  Symbols 


CHICAGO 
POPULAR  MECHANICS  COMPANY 

PUBLISHERS 


Copyright,  1919 

By 
H.  H.  WINDSOR 


CONTENTS 


CHAPTER  I 
Introductory    7 

CHAPTER  II 
The    Draftsman's    Equipment n 

CHAPTER  III 
Geometric   Exercises   with   Instruments 17 

CHAPTER  IV 
Working   Drawings 58 

CHAPTER  V 
Conventions   Used   in    Drafting 70 

CHAPTER  VI 
Modified   Positions  of  the   Object 77 

CHAPTER  VII 

The  Detailed  Working  Drawing 81 

CHAPTER  VIII 
Pattern-Workshop   Drawings    92 

CHAPTER  IX 
Penetrations no 

CHAPTER  X 
The   Isometric   Working   Drawing 121 

CHAPTER  XI 
Miscellaneous  Exercises ' 126 

CHAPTER  XII 
A  Suggested  Course  for  High  Schools 156 


REFERENCE  VOCABULARY 

FOR  the  benefit  of  those  who,  for  the  first  time,  may  meet 
new  terms  and  expressions  in  this  manual,  the  following 
vocabulary,  with  definitions,  is  appended : 

Altitude.     Vertical  height. 

Angle.     Space  between  two  intersecting  lines. 

Apex.     Point  where  converging  lines  meet. 

Apices.     More  than  one  apex. 

Arc.     Any  part  of  the  circumference  of  a  circle. 

Area.     Surface  in  units  of  measurement. 

Bisect.     To  cut  in  two  equal  parts. 

Bisector.     A  line  which  bisects. 

Chord.  The  line  connecting  any  two  points  of  an  arc  of  a 
circle. 

Circumference.    The  boundary  of  a  circle. 

Circumscribe.    To  draw  around. 

Convention.  Customary  method  or  symbol  used  in  pro- 
ducing a  drawing. 

Decagon.     Figure  of  ten  sides  and  ten  angles. 

Degree.     One  36oth  part  of  a  circle. 

Diameter.  The  distance  measured  across  the  center  of  a 
circle  or  a  line  drawn  through  the  center  terminating  in  the 
circumference. 

Element.     A  part  which  goes  to  make  up  the  whole. 

Elevation.     A  view  of  an  object  looking  at  the  front  or  side. 

Elliptical.     Pertaining  to  the  shape  of  an  ellipse. 

Equilateral.     Equal-sided. 

Frustum.  Remaining  portion  of  a  cone  or  pyramid  when 
the  top  has  been  removed  parallel  to  the  base. 

Hemisphere.     Half  a  sphere. 

Heptagon.     Figure  of  seven  sides  and  seven  angles. 

Hexagon.     Figure  of  six  sides  and  six  angles. 

Horizontal.     Parallel  to  the  horizon. 

Hypotenuse  (spelled  also  Hypothenuse).  The  diagonal 
distance  between  opposite  angles  of  a  rectangle  or  the  side 
opposite  the  right  angle. 

Isometric.     Of  equal  measurement. 

Isosceles  Triangle.  A  triangle  with  two  sides  of  equal 
length  and  base  angles  equal. 

Lateral.     Side. 

IV 


REFERENCE  VOCABULARY 


Line.    That  which  has  length  only. 

Median.  Line  drawn  from  the  vertex  of  an  angle  to  the 
middle  point  of  the  opposite  side  of  a  triangle. 

Nonagon.     Figure  of  nine  sides  and  nine  angles. 

Octagon.     Figure  of  eight  sides  and  eight  angles. 

Orthographic.  Derived  from  two  Greek  words,  orthos, 
straight  and  graph,  to  write.  Hence  applied  to  a  straight-line 
drawing  determined  by  projection  on  H,  V  and  P. 

Parallel.  Lines  or  planes  are  said  to  be  parallel  when  all 
ooints  of  one  are  equally  distant  from  all  points  of  another. 

Parallelogram.  A  four-sided  figure  with  opposite  sides  par- 
allel and  of  equal  length. 

Pentagon.     Figure  of  five  sides  and  five  angles. 

Perimeter.    The  distance  measured  around. 

Perpendicular.     Any  line  at  right  angles  to  another. 

Pi  (T).  A  Greek  letter  used  as  a  convenient  symbol  to 
express  the  relation  between  diameter  and  circumference.  if 
—  3.1416.  The  diameter  of  a  circle  X  *"  =  circumference. 

Plan.     A  view  looking  down  upon  the  top. 

Plane.     A  surface  with  length  and  width  and  no  thickness. 

Plinth.  A  prism  whose  height  is  less  than  any  one  of  its 
other  dimensions. 

Point.     That  which  has  position  only. 

Polygon.    A  plane  figure  bounded  by  four  or  more  sides. 

Prism.  A  figure  bounded  by  rectangular  faces,  two  of  which 
are  parallel. 

Project.    To  point  toward. 

Pyramid.  A  solid  with  triangular  faces  converging  to  a 
common  vertex. 

Quadrant.     The  fourth  part  of  a  circle. 

Quadrilateral.     A  four-sided  polygon. 

Radius.     Half  the  diameter. 

Radii.     The  plural  form  of  radius. 

Rectangle.  A  plane  figure  with  four  right  angles  of  90° 
each. 

Rectify.     To  make  straight  or  right. 

Rectilinear.     Pertaining  to  right  or  straight  lines. 

Rotate.    To  roll. 

Scalene  Triangle.  A  triangle  all  sides  of  which  are  unequal 
in  length. 

Section.    A  view  determined  by  a  cutting  plane. 
V 


REFERENCE  VOCABULARY 

Sector.  A  radial  division  of  a  circle  or  the  space  between 
two  radial  elements. 

Segment.     The  space  between  the  chord  and  arc  of  a  circle. 

Semi-circle.     Half  a  circle. 

Sphere.  Ball  or  globe.  A  solid  with  all  points  of  the 
surface  equally  distant  from  a  point  within,  called  the  center. 

Tangent.    To  lie  adjacent  at  a  single  point. 

Triangle.     A  three-sided  figure. 

Trisect.     To  cut  into  three  equal  parts. 

Truncate.     To  cut  off. 

Vertex.     A  common  point  of  several  converging  lines. 

Vertical.     Always  straight  "up  and  down." 


DEFINITIONS  OF  SYMBOLS 

2irR    Circumference  of  a  circle  when  R  =  radius. 

7rR2     Area  of  a  circle  when  R  =  radius. 

1     Perpendicular. 
||      Parallel. 

=    Means  "equals"  or  "is  equal  to". 

A.     Angles. 

X     Intersecting,  or  multiplied  by,  as  the  case  may  be. 

.'.     Therefore. 

L    Right  angle.     Two  intersecting  lines  making  90°  to  each 
other. 

Z     Acute  angle.     Two  intersecting  lines  less  than  90°  to  each 
other. 

X —  Obtuse  angle.     Two  intersecting  lines  more  than  90°  to 
each  other. 

H    Horizontal. 

V    Vertical. 

P     Profile. 

GL    Ground  line. 

VL    Vertical  line. 


VI 


PRACTICAL   MECHANICAL 
DRAWING 

CHAPTER  I 

INTRODUCTION 

"JV/TECHANICAL  drawing  is  one  of  the  most  popular 
*•*•*•  and  most  profitable  subjects  of  study  for  the  boy 
or  young  man  of  today.  It  is  an  essential  qualification 
in  most  lines  of  engineering,  an  almost  indispensable 
accomplishment  in  many  occupations,  and  often  the 
secret  of  successful  advancement.  It  is  founded  upon 
the  science  of  geometry,  which,  as  applied  to  drawing, 
becomes  a  delightful  and  interesting  subject,  and  not 
the  difficult  study  the  beginner  fears.  For  illustration, 
a  farmer  wishes  to  know  how  many  gallons  of  water 
will  fill  a  tank,  the  diameter  and  height  being  known ; 
how  many  bushels  of  wheat  will  fill  a  bin,  or  how  many 
acres  there  are  in  a  field  a  quarter  of  a  mile  square. 
These  examples,  like  many  others,  illustrate  the  prac- 
tical application  of  geometry,  a  subject  no  less  impor- 
tant to  the  mechanic  than  the  farmer,  but  a  thousand 
times  more  interesting  to  the  student  than  the  usual 
text  book. 

In  preparing  this  manual  the  author  was  ever  mind- 
ful of  the  many  circumstances  and  limitations  which 
have  so  often  combined  to  deny  to  aspiring  youth  the 
advantages  of  a  complete  education.  In  this  day  and 
age  competition  and  industrial  conditions  demand  the 
best  training  and  skill  for  every  productive  effort. 
What  the  artisan  or  mechanic  does  to  improve  himself 


8  A  PRACTICAL  COURSE  IN 

intellectually,  to  this  end,  increases  his  efficiency  and 
value  to  his  employer  in  every  respect. 

In  geometry  a  student  is  concerned  with  the  theorem 
of  a  problem,  and  the  proof,  or  why  it  is  so.  In  me- 
chanical drawing  the  mechanical  operations  of  con- 
struction— the  actual  doing  of  a  problem,  graphically, 
by  the  use  of  compass,  triangles  and  other  instruments 
— is  considered  essential  and  sufficient.  However,  this 
course  does  not  preclude  a  master's  knowledge  of  the 
principles  of  geometry.  Any  live,  wide-awake  boy  can 
apply,  to  a  good  advantage,  these  geometric  exercises 
to  some  project  which  he  desires  to  work  out  or  invent, 
without  first  having  studied  the  subject. 

The  surveyor  with  his  tape  and  transit,  the  architect 
or  mechanical  engineer  with  his  slide  rules  and  for- 
mulas, must  know  these  exercises  also.  If  a  craftsman 
desires  a  brace  or  bracket  for  a  plate  rail,  he  must  know 
how  to  "lay  out"  the  desired  curves  and  angles.  If  a 
boy  desires  to  make  a  taboret  or  jardiniere-stand  with  a 
hexagonal  or  octagonal  top,  he  must  first  solve  the  geo- 
metric problem  or  consequently  be  unhappy  with  the 
results. 

One  reason  for  not  accepting  a  freehand  perspective 
sketch  as  a  substitute  for  the  geometric  drawing  lies  in 
the  fact  that  the  sketch  seldom  shows  all  the  informa- 
tion required  for  the  workman.  The  sketch  deals  with 
outward  appearances  only  and  from  one  viewpoint. 
The  mechanical  drawing  of  an  object  delineates  the 
actual  facts,  within  or  without,  and  from  as  many  view- 
points as  the  object  has  dimensions.  Any  hidden  or  de- 
tailed information  is  considered  as  important  as  that 
which  is  visible,  and  these  details  are  represented  ac- 
cordingly by  suitable  conventions,  the  word  convention, 


MECHANICAL  DRAWING  9 

in  drafting,  meaning  a  customary  symbol  or  method 
established  by  precedent. 

The  freehand  sketch  is  governed  by  well-known 
laws  of  perspective  which  constitute  the  language  of 
the  artist  from  the  esthetic  standpoint.  The  mechan- 
ical drawing  is  represented  by  customary  shop  and 
drafting-room  conventions  and  is  the  language  of  the 
mechanic  and  artisan.  The  one  develops  the  power  of 
observation,  good  judgment  and  individuality;  the 
other,  precision,  accuracy  and  mechanical  ability. 

An  advantage  that  the  mechanical  drawing  has  over 
the  sketch  is  that  the  workman  will  not  be  apt  to  con- 
fuse apparent  dimensions,  as  seen  from  the  perspect- 
ive, with  true  measurements,  as  seen  from  the  work- 
man's drawing.  All  working  drawings  are  made  to 
scale,  and  all  dimensions  are  proportional  and  properly 
placed.  They  must  be  made  in  such  a  manner  that 
the  "dumbest"  man  in  the  shop  will  understand  them. 
Otherwise,  if  an  error  occurs  in  construction,  the  blame 
attaches  to  the  draftsman.  Such  a  drawing  must  keep 
in  mind  all  those  who  must,  of  necessity,  use  it.  Me- 
chanics, designers,  engineers  and  artisans  of  any  trade 
fully  realize  the  importance  of  a  definite  plan  of  pro- 
cedure. Bridges,  buildings,  railroads  and  canals  must 
be  thought  out  on  paper,  and  their  feasibility  satis- 
factorily passed  upon,  before  a  mechanic  or  construc- 
tion company  begins  the  actual  work.  Perhaps  the 
most  important  part,  if  not  the  most  difficult,  is  the 
making  of  the  plans  and  specifications.  The  next  most 
important  part  is  working  according  to  the  direction  of 
the  plans. 

Constructive  drawing  also  finds  expression  in  a  mul- 
titude of  shops.  A  cabinetmaker,  machinist,  pattern- 
maker, or  contractor,  must  have  intelligent  pictures  or 


10  MECHANICAL  DRAWING 

drawings  to  guide  his  hands,  and  these  drawings  must 
be  accurate  and  clear.  A  draftsman,  whether  amateur 
or  professional,  who  fails  to  make  them  so,  may, 
through  ignorance  and  carelessness,  or  both,  cause  a  loss 
of  great  consequence  to  his  employer  and  the  world  at 
large.  Someone  has  said  :  "Mechanical  drawing  is  the 
alphabet  of  the  engineer ;  without  it  he  is  only  a  hand. 
With  it  he  indicates  the  possession  of  a  head."  It  is 
needless  to  say  that  the  hand  will  only  do  what  the 
head  directs. 

A  uniform  code  of  conventions  and  symbols  is  re- 
quired among  workmen  and  shops  just  as  among  tele- 
graph operators.  Such  a  language,  if  it  may  be  so 
called,  has  come  to  be  accepted  generally  among  drafts- 
men who  adhere  closely  to  the  modern  approved  forms, 
and  these  will  be  used  throughout  this  manual. 


CHAPTER  II 
THE  DRAFTSMAN'S  EQUIPMENT. 

*  I  HHE  old  saying  that  a  poor  workman  blames  his 
•*•  tools  is  very  nearly  if  not  always  true,  for  if  a 
workman  is  content  to  work  with  an  instrument  poor 
in  quality  or  poorly  kept,  it  must  be  taken  that  he  ex- 
pects to  do  poor  work.  How  can  a  draftsman  produce 
an  accurate  drawing  if  the  compass  legs  are  not  firm 
and  the  points  blunt,  T  square  nicked,  triangles  warped, 
pencil  dull,  ruling-pen  clogged  with  ink,  and  many 
other  possible  imperfections  which  would  mar  the 
finished  drawing?  Hence,  it  goes  without  saying  that 
to  do  commendable  work  one  must  have  good  mate- 
rials, take  excellent  care  of  them  and  keep  them  in  per- 
fect repair.  A  complete  list  is  appended  below,  though 
not  all  are  required.  Those  marked  with  stars  are 
essential ;  the  others  are  luxuries : 

*Drazviny-Board — 16x21  in.,  inlaid,  can  be  made  of 
A  No.  i  soft  white  pine  by  mortising  narrow  strips 
across  each  end  of  the  board.  The  size  is  not  arbitrary. 
Local  conditions  may  require  smaller  boards  and  thus, 
of  course,  smaller  plates.  Fig.  i. 

^Drawing-Paper — Whatman's  hot  or  cold-pressed 
(white)  paper.  Keuffel  &  Esser  or  E.  Dietzgen 
cream  paper,  size  12x16  in.  or  15x20  in.;  but  size  of 
board  and  paper  to  be  determined  by  local  conditions, 
per  above.  A  good  bond  paper  may  also  be  used.  Two- 
ply  bristol  paper  is  excellent.  For  Patent  Office  draw- 
ings three-ply  bristol  paper  is  required. 

^Thumb-tacks — Comet  No.  2  is  one  of  many  good 
tacks.  They  come  in  small  tin  cartons. 


12  A  PRACTICAL  COURSE  IN 

* Pencils — 2H  and  4.H.  Sharpen  so  that  the  lead  is 
exposed  y\  or  f  in. 

*  Erasers — Faber  No.  211,  Art  Gum,  Eberhard 
typewriter  ink  eraser,  or  others  as  good. 

*Scale — Ordinary  hardwood  rulers  will  do  at  first. 
A  triangular  boxwood  scale,  divided  into  different 
scales,  is  best. 

*T  Square — Should  be  as  long  as  the  board  and  made 
of  pear  wood.  Boys  can  make  this  in  the  wood  shop. 
Fig.  i. 

^Triangles — 30-60-90  celluloid,  8  in.  or  10  in.  long, 
45-90,  celluloid,  6  or  8  in.  long.  Wooden  triangles 
are  inaccurate.  Fig.  i. 

Emery  Pad — Or  No.  ooo  sand-paper,  to  sharpen 
pencils.  Each  pencil  should  be  sharpened  chisel- 
shaped  at  one  end  and  conical  at  the  other.  Use  a  2H 
or  4H-grade. 

^French  Curve — Celluloid.  Lead  curves  are  cum- 
bersome and  expensive. 

Case  or  set  of  Instruments — Containing: 
*i    compass    with    lead    and    pen    adjustment    and 
lengthening  bar. 

divider  (large). 

divider  (bowspring)  3  in.  long, 
ruling-pen  (large), 
ruling-pen  (small), 
bowspring  compass   (ink), 
bowspring  compass  (pencil), 
box  leads. 

protractor  (German  make  preferable), 
penholder  and  pen,  No.  506  and  No.  516,  ball- 
pointed. 


MECHANICAL  DRAWING 


13 


*i  bottle  Higgins'  water-proof  ink  (black). 

i  typewriter  erasing-shield  (celluloid  or  nickel- 
plated). 

These  instruments,  including  the  paper,  need  not  be 
expensive,  i.  e.,  those  marked  with  stars.  Cheap  brass 
sets  are  worse  than  useless.  If  it  is  convenient,  the 
purchaser  should  consult  with  a  practical  draftsman 
before  selecting  the  materials. 


Case  of  Instruments 
HOW   TO   USE   THE    MATERIALS 

1.  The  paper  should  be  tacked  in  the  upper  left- 
hand  corner  of  the  drawing-board  so  that  the  T  square 
may  not  slip  when  drawing  the  lowest  lines  on  the 
plate. 

2.  Thumb-tacks  should  not  be  withdrawn  by  the 
fingers.    Use  a  knife  blade  or  other  flat  instrument. 

3.  To   get   clean,    sharp   lines,   pencils    should   be 
sharpened  frequently,  but  under  no  circumstances  must 
ridges  be  made  on  the  drawing  by  heavy  pressure  on 
the  pencil. 


14  A  PRACTICAL  COURSE  IN 

4.  Use  a  soft  gum  eraser  to  clean  the  drawing  be- 
fore inking,  that  a  glossy  finish  to  black  lines  may  be 
retained.     Use  ink-erasers  for  pencil  lines  only  in  ex- 
ceptional cases  where  the  pencil  has  caused  deep  ridges 
in  the  paper.    All  division  lines  should  be  erased  before 
inking. 

5.  All  dimensions  should  be  stepped  off  from  the 
scale  or  ruler,  with  dividers,  and  then  pricked  lightly 
in  the  required  place  on  the  drawing.    Explanation  will 
be  given  later  as  to  how  to  scale  a  drawing  properly. 

6.  Always  use  the  upper  edge  of  the  T   square, 
which  should  be  held  against  the  left-hand  edge  of  the 
drawing-board.  Never  use  the  upper  edge  of  the  square 
as  a  cutting  edge.    The  least  nick  will  cause  inaccurate 
work  as  long  as  it  is  used  thereafter.    Fig.  i. 

7.  The  triangles,  which  are  used  to  draw  oblique 
and  perpendicular  lines,  should  rest  upon  the  upper 
edge  of  the  T  square.     Many  and  various  combina- 
tions of  angles  may  easily  be  made  by  combining  both 
the  30-60  and  45-90.     The  oblique  side  of  the  triangle 
should  always  be  to  the  right  while  in  use,  whether  in 
inking  or  penciling.    Fig.  I. 

8.  The  celluloid  irregular  curve  is  used  in  defining 
curves  which  are  impossible  to  obtain  with  the  compass. 
It  is  composed  of  many  curves,  but  has  seldom  the 
right  one,  so  that  it  is  often  necessary  to  shift  it  into 
many   positions   before   required   results   may  be   ob- 
tained. 

9.  Only  two  instruments  in  the  case  need  explana- 
tion, and  this  is  better  acquired  by  practice.    The  com- 
pass legs  are  jointed  so  that  the  nibs  of  the  pen  may  be 
square  to  the  surface  of,  the  paper  while  the  circle  is 
being  drawn.     The  hand  should  describe  the  circle 
above  the  paper  while  in  operation,  and  not  remain  sta- 


MECHANICAL  DRAWING 


15 


tionary.  The  ruling-pen  should  incline  slightly  in  the 
direction  of  the  line  and  should  be  held  so  that  the  nibs 
of  the  pen  are  not  in  contact  with  the  edge  of  the  T 
square.  To  keep  the  instruments  from  corroding, 
polish  them  with  a  small  chamois  skin  and  five  cents' 
worth  of  chalk  precipitate,  or  Spanish  whiting.  Instru- 


ment  must  be  kept  clean.  A  thin  piece  of  linen  should 
be  drawn  between  the  nibs  of  the  pen  after  each  using, 
as  the  air  congeals  the  ink  quickly.  The  pen  is  filled 
by  dropping  the  ink  from  the  quill, — which  is  in  the 
stopper  of  the  bottle, — while  being  held  in  a  vertical 
position.  It  should  never  be  filled  over  one-quarter 
inch.  Lines  are  ruled  from  Jeft  to  right  arid  bottom 
upward.  Use  the  adjusting  screw  to  get  the  desired 
width. 


16  MECHANICAL  DRAWING 

10.  The  German  protractor  is  a  semi-circular  in- 
strument graduated  into  180  degrees.    This  is  used  to 
obtain  angles  other  than  those  obtained  by  the  trian- 
gles. 

11.  Higgins'  inks  are  waterproof.     Should  a  blot 
occur,  first  erase  with  the  ink  eraser.     (Never  use  a 
knife.)     Second,  glaze  the  roughened  surface  by  using 
the  back  of  a  bonehandled  knife,  or  soapstone.    Third, 
"size"  the  glazed  surface  by  spreading  over  it  a  thin 
coat  of  graphite,  from  a  soft  pencil.    The  paper  is  now 
ready  to  re-ink. 


CHAPTER  III 

GEOMETRIC    EXERCISES    WITH    INSTRUMENTS 

Tf  XERCISE  i.— Bisect  a  line  of  any  length  and  arc 
*-^  of  suitable  radius.  Construction:  With  radius 
greater  than  one-half  of  AB  and  points  A  and  B  as  cen- 
ters describe  intersecting  arcs  at  i  and  2.  If  a  line  be 
drawn  from  i  to  2  it  will  bisect  AB.  Fig.  2. 


Fig.  2 


Exercise  2. — Erect  a  perpendicular  to  a  given  line 
(Problem  i.)  Fig.  2.  Second  method.  Construction: 
From  a  given  point  E  outside  the  given  line  AB  draw  a 
line  at  any  angle  to  AB.  Bisect  and  inscribe  a  circle 


18 


A  PRACTICAL  COURSE  IN 


about  ED.     Where  the  circle  cuts  AB  is  a  point  of  the 
_L  through  point  E.     Figs.  2  and  3. 

Exercise  J. — To  draw  a  //  line  through  a  given  point 
X  to  a  given  line  AB.    Construction :    From  any  point 


Fie.  3 

B  on  the  given  line  and  a  radius  equal  to  BX  describe 
arc.  From  X  and  same  radius  describe  a  similar  arc 
through  B.  Lay  off  BY  on  second  arc  =  to  AX.  A 
line  drawn  through  X  and  Y  is  //  to  AB.  Fig.  4. 

Second  method.    Construction :  Draw  a  line  making 
any  angle  with  AB.    With  C  as  center  and  any  radius 


Fig.  4 


MECHANICAL  DRAWING 


19 


Fie.  5 


Fie.  6 


Fie.  7 


20  A  PRACTICAL  COURSE  IN 

describe  an  arc  making  angle  0.  Duplicate  this  angle 
with  given  point  as  center.  Fig.  4. 

Exercise  4. — Divide  two  lines  into  proportional  parts. 
Construction :  Lay  off  one  line  into  any  number  of 
divisions.  Connect  the  extremities  of  each  line.  By 
means  of  triangles  draw  parallels  through  remaining 
points.  Fig.  5. 

Exercise  5. — Construct  tangents  to  a  given  arc  of 


Fig.  8 

any  radius.  Construction :  With  any  radius  describe 
arc  of  a  circle.  From  the  center  of  the  arc  to  any  point 
of  the  circumference  draw  a  radial  line.  At  the  ex- 
tremity of  the  radial  on  the  circumference  erect  a  1. 
This  is  the  required  tangent.  Fig.  6. 

Exercise  6. — Duplicate  and  bisect  a  given  angle. 
Construction :  Draw  any  two  intersecting  lines, 
making  any  convenient  angle.  To  duplicate,  draw  CD 
with  any  length.  Describe  an  arc  cutting  given  angle 
at  A  and  E.  With  same  radius  describe  arc  cutting  CD 
at  F.  Lay  off,  with  F  as  center,  the  distance  AE,  and 
draw  the  other  side  of  angle  through  C  and  G.  Bisect 
as  in  Exercise  i.  Fig.  7. 


MECHANICAL  DRAWING 


22  A  PRACTICAL  COURSE  IN 

Exercise  /. — To  draw  angle  of  60°.    Construction: 
With  any  line  as  a  base  and  any  point  therein  as  a  cen- 
ter, describe  an  arc  of  any  convenient  radius,  cutting 
the  base  line  at  C.    With  C  as  a  center  and  radius  AC 
describe  arc  at  E.    A  line  through  AE  is  60°  to  AB. 
Bisect  to  get  angle  of  30°.    Other  angles  can  be  easily 
determined.    22°  30'  reads  22  degrees  and  30  minutes 
or  22%  degrees.    (Fig.  8.)    The  table  is  as  follows: 
60"  (seconds)  =  i  minute  ('). 
60'   ( minutes )=  i  degree  (°). 

360°  (degrees)  =  i  circle. 

[Note  the  characters  ('  and  ")  used  to  designate 
minutes  and  seconds  are  used  also  to  designate  feet  and 
inches.  The  context  will,  however,  generally  avoid 
confusion  as  to  their  meaning.] 

Can  any  angle  be  trisected  ? 

.  Exercise  8. — By  triangles  only,  divide  a  semicircle 
into  angles  of  15°.  Use  T  square  as  a  base  for  the  tri- 
angles. Fig.  9. 

Exercise  9. — Rectify  a  quadrant  of  a  circle.  Ap- 
proximate methods.  Construction :  Draw  a  circle  of 
any  suitable  diameter  and  divide  into  quadrants.  Draw 
a  tangent  of  indefinite  length  at  lower  end  of  CD. 
Through  A  draw  a  line  making  60°  to  this  tangent. 
Where  it  cuts  BD  determines  the  length  of  the  arc  AD. 
Any  smaller  arc  can  be  determined  by  extending, 
through  C  and  the  other  end  of  the  given  arc,  a  line  to 
BD.  Fig.  10.  Second  method.  Approximate.  Fig. 
u.  AE  —  BD,  Fig.  10. 

Exercise  10. — Construct  a  right-angle  triangle  one 
angle  of  which  is  30°.  The  sum  of  all  angles  of  any 
triangle  is  180°.  If  a  right  angle  is  90°,  what  must  the 
remaining  angles  be  ?  This  exercise  is  applicable  as  an 


MECHANICAL  DRAWING 


23 


aid  in  determining  the  pitch  or  length  of  a  rafter,  when 
the  rise  and  run  are  given.  Pythagoras  discovered  the 
principle  that  the  square  of  the  rise  -|-  the  square  of  the 
run  equals  the  pitch  squared :  X2  -f-  Y2  =  Z2.  Fig.  12. 


Fie.   11 

Exercise  n. — To  find  approximately  the  distance 
across  an  unknown  area  by  means  of  similar  right 
angles.  Construction :  Select  a  tree  or  object  on  the 
opposite  bank  or  side  as  indicated  at  A.  Select  another 


on  this  side,  say  D.  Lay  off  a  convenient  distance  from 
D  to  C  in  the  line  ADC.  Select  a  point  B  at  right  an- 
gles to  AD  and  construct  a  parallelogram  BODC.  De- 
termine point  X  on  the  ground  which  is  in  line  with  OC 


24  A  PRACTICAL  COURSE  IN 

and  BA  and  measure  the  distance  XO.    By  proportion, 

BDXBO 

AD  :  BD  :  :  BO  :  XO  .'.  AD  =  

XO 

Lay  out  the  diagram,  substituting  known  values  for 
BD  and  DC  and  solve.     Fig.  13. 


Exercise  12. — Equilateral  triangle.  Construction : 
Assume  any  length  for  a  base.  With  a  radius  equal  to 
the  length  of  base  and  each  terminal  A  and  B  as.  cen- 
ters describe  intersection  at  X.  Connect  this  point  by 
lines  to  C  and  D.  Measure  the  angles  of  an  equilateral 
triangle  in  degrees.  What  is  their  sum  ?  Stained-glass 
windows  are  often  laid  out  in  Gothic  arch  forms  by 
this  kind  of  triangle.  Fig.  14. 

Exercise  13. — Isosceles  triangles.  Construction :  On 
a  line  of  given  or  assumed  lengths  and  with  a  radius 


MECHANICAL  DRAWING 


25 


Fie.  14 

greater  or  smaller  than  AB  proceed  as  in  the  problem 
above.  Are  all  the  angles  equal?  What  is  their  sum? 
Fig.  15- 

Exercise  14. — The  vertex  angle  of  an  isosceles  tri- 
angle is  150°,  and  its  base  is  3  inches  long.  Without 
protractor  make  a  drawing.  The  trilium  is  an  early 


fig.  15 


26  A  PRACTICAL  COURSE  IN 

spring  flower  shaped  on  the  order  of  an  isosceles  tri- 
angle. 

Exercise  15. — Scalene  triangle.  Base  2l/2  inches, 
and  base  angles  22]/2°  and  37^°  respectively.  What 
is  the  sum  of  the  angles?  Of  any  triangle?  Fig.  16. 

Exercise  16. — Inscribe  a  square  within  a  3  inch 
circle.  Without.  Fig.  17. 

Exercise  17. — Circumscribe  a  square  about  the  circle 
in  the  problem  above.  What  is  the  relation  of  inner  to 


Fie.  16 

outer  square?  The  syringa  is  a  four-petaled  flower 
shaped  like  a  square. 

Exercise  18. — Pentagon  within  a  circle.  Construc- 
tion: Bisect  the  diameter  of  the  circle.  Bisect  a  ra- 
dius. With  C  as  center  and  AC  as  radius,  describe  arc 
at  B.  With  A  as  a  center  and  AB  as  a  radius,  describe 
arc  on  the  given  circle  at  D.  AD  is  the  length  of  one 
side  of  the  polygon.  Lay  off  remaining  sides  and 
draw  a  star.  Fig.  18. 

What  is  the  size  of  an  interior  angle?  Use  pro- 
tractor. 


MECHANICAL  DRAWING 


27 


Fig.  17 


Fig. 


28 


A  PRACTICAL  COURSE  IN 


Exercise  19. — Pentagon.  Construction:  Base  il/^-'m. 
With  one  radius  =  to  the  base  length  describe  arcs 
from  centers  I,  2  and  3.  Connect  I  and  2  with  7  and 
8  and  complete  the  pentagon.  Inscribe  a  circle  within 


Fi£T.  19 


the  figure.  Circumscribe  a  circle  about  the  polygon. 
Many  flower  forms — pansy,  violet — are  pentagonal  in 
shape.  Fig.  19. 

Exercise  20. — Hexagon.  Within  a  circle.  Construc- 
tion :  Lay  off  the  radius  six  times  on  the  circumfer- 
ence of  the  circle  and  connect  the  points.  Without  the 
protractor,  what  is  the  interior  angle  of  this  polygon? 


MECHANICAL  DRAWING  29 

Use  this  key :    2n  —  4  right  angles  when  n  =  the  num- 
ber of  sides  of  the  polygon. 

(2X6)— 4X90° 

=  120° 

n 

Prove  this  to  be  true.    Draw  a  six-pointed  star.    Fig. 
20. 


Fie.  20 

Exercise  21. — Hexagon  by  means  of  the  30-60  tri- 
angle. The  hexagonal  bolt  is  an  illustration  of  the  use 
of  the  hexagon.  Fig.  20. 

Exercise  22. — Hexagon  without  a  given  circle.    Fig. 

21. 

Exercise  23. — Heptagon  within  a  circle.  Construc- 
tion. Draw  a  line  making  any  angle  with  AB.  Divide 
AB  into  as  many  equal  divisions  as  the  polygon 
has  sides.  With  A  and  B  as  centers  and  AB  as  a  radius 


30 


Fig-  22 


MECHANICAL  DRAWING 


31 


describe  arcs  at  C.  A  line  drawn  through  C  and  2, 
cutting  the  circle  at  D,  determines  the  length  of  one 
side  of  the  heptagon.  This  method  will  apply  to  any 
polygon.  Use  above  formula  to  determine  the  size  of 
the  interior  angle.  Fig.  22. 


Fig.  23 

Exercise  24. — Octagon  within  a  circle.  Construc- 
tion :  Within  a  circle  of  an  assumed  diameter,  divided 
into  quadrants,  draw  bisectors.  The  circumference  is 
now  divided  into  eight  equal  divisions.  Determine  and 
locate  the  size  of  the  interior  angle  by  the  preceding 
formula.  Fig.  23. 

Exercise  25. — Octagon  within  a  square.     Fig.  23. 

Exercise  26. — Combination  of  polygons  on  a  given 
base  of  I  inch.  Construction :  Proceed  as  in  laying 
out  a  hexagon.  Bisect  the  arc  A-2.  Trisect  2-B.  With 
center  2,  draw  arcs  cutting  through  C  and  D  at  i  and  3. 


32  A  PRACTICAL  COURSE  IN 

Points  i  and  3  are  centers  of  circles  circumscribing 
polygons  of  the  required  number  of  sides.  Fig.  24. 

Exercise  27. — Inscribe  circles  about  the  triangles 
given  in  problems  10,  12,  13  and  15. 

E.rercise  28. — Inscribe  three  circles  in  the  triangle 
given  in  Problem  12.  Construction:  Draw  the  me- 
dians of  each  side  or  bisect  each  interior  angle.  Bisect 
angle  AC.  Where  the  bisector  cuts  the  line  OX  is  the 
center  for  one  circle.  Fig.  25. 

Exercise  29. — Five  circles  tangent  to  a  given  circle 
and  each  other ;  within  or  without  the  given  circle. 
Construction :  Divide  the  given  circle  into  five  equal 
parts  and  bisect  each  sector.  The  centers  of  each  circle 
will  be  located  on  the  bisector.  Draw  a  tangent  at  the 
terminal  of  a  bisector  and  extend  it  until  it  cuts  a  radial 
line.  Bisect  the  angle  this  tangent  makes  with  the  ra- 
dial and  extend  this  bisector  until  it  cuts  AB  at  C, 
which  is  the  center  of  one  circle.  Fig.  26. 

Exercise  jo. — A  circle  tangent  to  a  given  circle  and 
a  given  line.  Construction :  With  the  radius  of  the 
required  circle  added  to  the  radius  of  the  given  circle, 
and  C  as  a  center,  strike  an  arc  1-2.  Draw  a  line  paral- 
lel to  the  given  line  with  the  distance  =  to  the  radius 
O  of  the  required  circle.  Where  this  line  and  arc  1-2 
intersect  is  the  center  E  for  the  required  circle. 
Fig.  27. 

Exercise  31. — A  shaft  il/2  inches  in  diameter  rotates 
within  a  ball-bearing  consisting  of  10  tempered  steel 
balls.  Make  a  drawing  illustrating  size  of  balls  re- 
quired. Fig.  28.  Approximate.  Construction:  Pro- 
ceed as  in  problem  29  except  that  the  tangent  circles  are 
external  to  the  given  circle. 

Exercise  32. — Four  largest  circles  that  can  be  drawn 
within  a  square. 


MECHANICAL  DRAWING 
C 


33 


Fig.  23 


34  A  PRACTICAL  COURSE  IN 


Fig.  26 


Fie.  27 


MECHANICAL  DRAWING  35 

Exercise  55. — A  Maltese  cross.  Fig.  29.  Construc- 
tion :  Draw  two  equal  circles  upon  the  two  diameters 
of  a  given  large  circle  and  proceed  as  indicated  in  the 
drawing. 

Exercise  34. — Draw  a  geometric  border  using  the 
circle  as  a  unit.  Nearly  all  design  is  geometric  in  char- 
acter. Fig.  30. 


Exercise  35. — Figure  31  is  an  original  illustration 
of  the  Swastika. 

Exercise  ^6. — Geometric  monogram  within  a  trefoil. 
Fig.  32. 

Exercise  j/. — Moldings,  i.  Cyma  Recta,  Fig.  33. 
2.  Roman  Ogee,  Fig.  34.  3.  Scotia,  Fig.  35.  4. 
Echinus,  Fig.  36.  Ogee  Arch,  Fig.  37. 


36  A  PRACTICAL  COURSE  IN 


Fie-  30 


Fie.  29 


Fig.  31 


MECHANICAL  DRAWING  37 


38  A  PRACTICAL  COURSE  IN 


Fig.  34 


Fie.  35 


Fig.  36 


MECHANICAL  DRAWING  39 

Exercise  ^8. — The  astronomer  tells  us  that  the  plane 
of  the  earth's  orbit  is  called  the  "ecliptic."  This  is  an 
ellipse  in  shape.  Draw  an  ellipse  by  two  methods.  The 
upper  half  to  be  constructed  as  follows :  AC=4}6 
inches.  DE  =  3^  inches.  DM  =  AB.  M  and  F  are 
centers  of  all  arcs  on  the  ellipse.  From  C  as  center  lay 
off  on  BC  any  number  of  points,  i,  2,  3,  4,  5,  etc.  With 
C-i  as  a  radius  and  M  and  F  as  centers  describe  arcs. 


Fiff,  37 

With  A-i  as  a  radius  and  MF  as  centers  describe  arcs 
intersecting  C-i.  These  are  points  of  the  ellipse.  Pro- 
ceed until  enough  points  are  determined  to  locate  the 
curve. 

The  lower  half  by  the  circle  method  is  self-evident 
from  the  illustration.  Fig.  38. 

Exercise  jp. — Trammel  method.  Fig.  39.  Con- 
struction :  Lay  off  on  a  small  strip  of  cardboard  the 
semi-minor  and  semi-major  axes  equal  to  the  dimen- 
sions of  the  above  problem.  Move  the  point  C  so  that 
it  is  always  on  the  line  AB  and  the  point  E  on  DF.  By 


A  PRACTICAL  COURSE  IN 


Fie.  39 


MECHANICAL  DRAWING 


41 


changing  the  position  of  the  trammel  frequently,  suf- 
ficient points  can  be  located  at  G,  on  the  trammel,  to 
determine  a  symmetric  ellipse.  Make  GC  =  DH  and 
GE  =  AH. 

Exercise  40. — Make  a  full-size  drawing  of  the  ellip- 
tic cam.    Fig.  40. 


Fig.  40 

Exercise  41. — A  point  on  a  connecting  rod  of  a  sta- 
tionary engine  describes  an  elliptic  curve  in  one  revo- 
lution of  the  crank  wheel.  With  B  as  the  given  point 
lay  out  the  desired  curve.  The  construction  for  the 
mechanism  may  be  omitted.  Fig.  41. 

Exercise  42. — Five-point  elliptic  arch  with  three 
radii.  Construction :  AB,  the  altitude,  and  CD,  the 
span,  are  given.  Lay  off  the  major  and  semi-minor 


42  A  PRACTICAL  COURSE  IN 


Fie.  41 


MECHANICAL  DRAWING  43 

axes.  With  A  as  a  center  and  AB  as  a  radius,  draw 
an  arc  through  BE.  Bisect  CE  at  F  and  describe  an 
arc  with  CF  as  radius.  CG  =  AB  and  is  1  to  CDt 
G-3  is  1  to  BC,  and  where  G-3  intersects  CD  at  i  is  a 
point  of  the  first  center  of  the  ellipse.  Where  it  cuts 
AB  at  3  is  another.  Make  AH=BK.  With  3  as  a 
center  and  3~H  as  a  radius  describe  an  arc  through  H. 
With  C  as  a  center  and  AK  as  a  radius  strike  an  arc  at 


/ 


v  v/v  y  \  \  \  / 


y  y  y  y  /\/  y 


Fie.  43 

N.  With  I  as  a  center  and  i-N  as  a  radius  strike  arc 
at  2,  which  is  another  point  of  a  center  for  the  ellipse. 
With  the  construction  duplicated  on  the  right  of  the 
illustration  the  remaining  centers  are  determined. 
Points  i,  2,  3,  4  and  5  are  the  required  centers,  and  all 
arcs  and  facing  stones  radiate  from  their  respective 
centers.  Fig.  42. 

Exercise  43. — Cycloid.  Fig.  43.  A  curve  generated 
by  the  motion  of  a  point  on  the  circumference  of  a 
circle  which  rolls  on  a  straight  line  is  called  a  cycloid. 
The  figure  clearly  illustrates  the  construction.  Im- 
agine the  rolling  circle  to  be  the  end  of  a  cylinder. 

Exercise  44. — Epicycloid.  Fig.  44.  An  epicycloidal 
curve  is  generated  by  the  motion  of  a  point  on  the  cir- 
cumference of  a  circle  which  rolls  upon  a  circle. 

Exercise  45. — Hypocycloid.  Fig.  45.  A  hypocy- 
cloidal  curve  is  generated  by  the  motion  of  a  point  on 


44 


A  PRACTICAL  COURSE  IN 


Fig.  44 


the  circumference  of  a  circle  rolling  upon  the  concave 
side  of  a  circle.  Should  the  diameter  of  the  generating 
circle  =  the  radius  of  the  larger  circle  the  hypoey- 
cloid  would  become  a  straight  line. 

These  curves  are  used  in  constructing  the  profile  of 
gear  teeth.  Fig.  46  is  a  draftsman's  method  of  laying 
out  the  forms  of  teeth  theoretically,  the  method  to  the 
right  being  involute,  and  that  to  the  left,  cycloidal.  Fig. 
46a  is  a  perspective  sketch  of  the  same  from  a  pattern 
made  by  a  patternmaker  in  the  shop.  The  size  of  the 
rolling  circle,  2E,  in  determining  the  epi-  and  hypocy- 
cloidal  curves  is  not  a  fixed  diameter;  however,  it  is 


Fig.  45 


MECHANICAL  DRAWING 


best  to  make  it  one-half  the  diameter  of  the  pitch  circle 
of  the  smaller  of  two  engaging  gears.  In  a  problem 
where  the  diameter  of  PC,  or  2JR^,  and  the  number  of 
teeth  n  are  given,  the  circular  pitch,  which  is  the  dis- 


Fig.  46 


BASE  LINE- 
PITCH  LINE 
15° INVOLUTE  LINE 


46  A  PRACTICAL  COURSE  IN 

tance  from  one  tooth  to  a  corresponding  point  of  an- 
other, CP,  must  be  laid  off  first  on  PC.  The  involute 
method  is  as  follows :  At  the  radial  line  2  draw  a 
tangent  8  where  it  intersects  the  base  circle  at  2. 
Lay  off  on  this  tangent  the  chord  of  the  arc  of  the  PC 
between  radials  i  and  2.  This  is  a  point  of  the  curve 


Fig.  46a 

of  the  tooth.  Again  at  radial  3  repeat  the  above 
process,  but  lay  off  two  chords  of  the  arc  on  tangent 
9  instead  of  one;  on  10  three  chords,  and  so  on 
until  enough  points  are  secured  to  define  the  desired 
involute  tooth  curve.  Reverse  the  operations  for  the 

CP 
other  side.     -  -  =   the  width  of  the  tooth  or  space 

2 

for  all  purposes  in  drafting.  The  lower  half  of  the 
profile  of  the  tooth  is  a  radial  line.  The  base  circle 


MECHANICAL  DRAWING  47 

is  drawn  tangent  to  the  involute  line  of  15°,  through  M. 

Practically  the  same  principle  is  involved  in  laying 
out  the  cycloidal  tooth  except  that  the  chords  of  arcs 
on  PC  are  laid  off  on  the  arcs  of  the  rolling  circle. 
Above  the  line  PC  the  rolling  circle  generates  the  epi- 
cycloidal  profile,  or  addendum,  while  below,  the  hypo- 
cycloidal  or  dedendum.  A  =  E. 

The  following  additional  data  are  given  for  those 
who  would  like  to  specialize  on  gear  teeth  and  is  ar- 
ranged from  Kent,  a  well  known  authority : 
Addendum  =  depth  of  tooth  above  PC  —  .35  CP. 
Dedendum  =  depth  of  tooth  below  PC  =  .35  CP. 
Clearance  at  root  of  space  =  .05  to  .1  of  CP.  (C.) 
Actual  thickness  of  tooth  on  PC  =  .45  of  CP.  |    ^ 
Actual  width  of  space  on  PC  =  .55  of  CP.         f 

Backlash,  or  play  between  engaging  teeth  —  .1  of 

Circular  pitch  =  a  tooth  and  space  on  PC  and  is 
more  commonly  used  than  diametral  pitch. 

Diametral  pitch  =  a  certain  number  of  teeth  per 
inch  of  diameter  of  PC. 

If  DP  =  i  CP  ==  3.1416. 

=  iy2  =  2.094. 

—  2.  =  1.571. 
=  2%  =  1.396. 
=  2*/2  =  1.257. 

From  the  above  it  is  seen  that  a  IT  (pi)  relation  exists 
between  circular  and  diametral  pitch,  i.  e.,  if  w  be  di- 
vided by  DP  the  result  will  be  CP;  or  if  TT  be  divided 
by  CP  the  result  will  be  DP. 


*Are  about  equal  in  machine  cut  gears. 


48  MECHANICAL  DRAWING 

Let  n  =  number  of  teeth. 

TrD 

CP  =  when  D  —  diameter  of  PC. 

H 
TrD 

~CP 

The  thickness  of  rim  D  =  .12  -(-  .4  CP. 
The  width  of  face,  W,  Fig.  460,  averages  2  to  2^2 
CP. 

The  diameter  of  hub  •=.  twice  the  diameter  of  shaft. 

Thickness  of  web  connecting  hub  and  rim  varies. 

Arms  are  used  on  larger  gears.  Holes  are  often 
drilled  through  the  web  to  lighten  the  weight  without 
destroying  the  efficiency  of  the  gear  wheel.  The  length 
of  the  hub  may  be  flush  with  the  rim,  but  is  usually 
34  inch  or  more  longer. 

The  "face"  of  a  tooth  is  the  distance  B  above 
PC.  The  "flank"  of  a  tooth  is  the  distance  B  be- 
low PC.  "K,"  Fig.  460,  shows  the  position  of  the 
core  print  used- in  molding  the  hole  for  the  shaft. 

Problem  i. — Draw  the  front  and  side  views  of  a 
gear  wheel  having  24  teeth,  2*4  diametral  pitch,  with 
epicycloidal  profile  of  teeth.  Scale,  full  size. 

Problem  2. — A  pinion  for  a  certain  gear  has  27 
teeth.  CP  is  1.571  inch.  Draw  forms  of  teeth  by  in- 
volute method.  Scale,  half  size. 

Note :  A  pinion  is  the  smaller  of  two  gears  acting 
together  and  should  not  have  less  than  12  teeth. 

Problem  5. — A  recent  examination  for  a  city  high- 
school  position  contained  the  following  question : 

Make  a  scale  shop  drawing  of  a  pair  of  meshing 


50  A  PRACTICAL  COURSE  IN 

gears  of  8  diametral  pitch.  One  gear  to  be  a  plain 
gear,  to  have  32  teeth,  i-inch  face,  i-inch  bore, 
one  hub  %  inch  long  and  to  be  the  driver.  The  follow- 
ing gear  to  be  a  web  gear  and  to  travel  at  two-thirds 
as  many  r.  p.  m.  (revolutions  per  minute)  as  the  driver. 
The  follower  to  have  a  5/1 6-inch  web,  ^4 -inch  rim  or 
backing  and  2-inch  hubs,  one  hub  being  flush  and  the 
other  %-inch  long.  Each  gear  to  be  held  on  the  shaft 
by  two  kinds  of  fastenings.  All  dimensions  and  de- 
tails, not  here  specified,  to  be  assumed  at  the  option  of 
the  draftsman  to  make  the  mechanism  of  ordinary 
and  reasonable  proportions.  Driver  and  follower  to 
be  designated.  Driver  to  be  finished  all  over  (f.  a.  o.)  ; 
follower  to  be  finished  (f.)  at  rim,  also  on  ends  and 
outside  of  hubs. 

Note :  Profile  of  teeth  not  necessary  for  cut  gears. 
Scale,  full  or  double  size. 

Exercise  46. — Archimedean  spiral  of  one  whorl. 
Construction:  With  a  radius  equal  to  the  rise  of  the 
spiral  AB,  and  A  as  a  center,  describe  a  circle.  Di- 
vide AB  into  as  many  equal  divisions  as  the  circle  has 
been  divided  into  sectors.  Lay  off  successive  arcs 
on  the  radials  and  draw  in. the  curve.  If  a  spiral  of 
2  whorls  is  desired  divide  AB  into  twice  as  many  parts 
as  for  one  whorl.  This  problem  represents  a  cross 
section  of  the  Nautilus,  a  sea  shell  described  by  Oliver 
Wendell  Holmes  in  "The  Chambered  Nautilus." 
Fig-  47- 

Exercise  47. — Heart  plate  cam.  Fig.  48.  The  con- 
struction for  this  common  object  may  be  derived  from 
Exercise  46  and  the  figure.  The  sewing-machine  bob- 
bin-winder is  one  of  several  applications  of  its  use. 

Exercise  48. — The  involute  spiral.  This  curve  is 
developed  by  unwinding  a  string  wrapped  about  a 


MECHANICAL  DRAWING  51 

cylinder,  the  end  describing  the  involute.  Construc- 
tion :  Lay  off  tangents  at  regular  intervals  to  the 
cylinder.  On  the  first  tangent  line  step  off  the  chord 
of  one  arc.  On  the  second  tangent,  two  chords ;  on 


Fig.  49 

the  third,  three,  etc.  Draw  the  curve  through  the 
points.  Fig.  49. 

The  involute  is  used  in  defining  the  tooth  curve  of  a 
gear  wheel. 

Exercise  49- — Helix.  Fig.  50.  A  definition  of  a 
helix  may  be  given  as  the  combined  vertical  and  hori- 


Fie.  50 


MECHANICAL  DRAWING 


53 


zontal  motion  of  a  point  about  a  right  line  as  an  axis, 
no  two  points  of  the  curve  lying  in  the  same  plane. 
The  upper  part  of  Fig.  50  shows  this  part  laid  out  apart 
from  its  application  to  the  screw  thread.  Construction : 
Lay  out  the  plan  and  elevation  of  the  thread  desired. 


54 


A  PRACTICAL  COURSE  IN 


Fie.  53 


MECHANICAL  DRAWING 


55 


Divide  the  half  section  of  the  plan  into  any  number 
of  equal  parts  and  divide  the  pitch  into  as  many.  The 
curves  are  ebvious  from  the  illustration,  which  is  a 
single  thread.  By  a  single  thread  is  meant  the  wind- 
ing of  one  screw  thread  about  the  bolt-cylinder.  A 
double  requires  two  threads  parallel  to  each  other;  a 
triple,  three,  and  a  quadruple,  four.  Fig.  55  represents 
a  conventional  method  of  showing  the  single  thread 
in  practice.  No  attention  is  paid  to  the  theoretical 
helical  curve  in  drafting;  however,  it  is  essential  to 
have  a  proper  understanding  of  it. 


Fig.  5+ 


Exercise  50. — Ionic  volute.  Figs.  51,  52,  53  and  54. 
Fig.  51  is  an  illustration  of  the  volute  spiral  of  an  Ionic 
capital  in  classic  architecture  (Fig.  54).  In  laying 


56 


A  PRACTICAL  COURSE  IN 


out  such  a  curve,  either  method,  Fig.  52  or  Fig.  53, 
may  be  used  with  the  same  results.  When  AB  is  given 
(Fig.  51),  make  the  eye  of  the  volute  1/16  of  AB  and 
locate  its  center  on  the  ninth  division  of  AB.  Divide 


,60 


Fig.  55 


the  semi-diagonal  of  the  square  into  three  equal  parts 
and  construct  squares  through  these  points,  as  in  Fig. 
52.  Each  corner  of  these  squares  is  a  center  for  quad- 
rants of  the  outer  spiral  starting  with  radius  A.  The 
inner  dotted  squares  are  drawn  to  pair  within  the 
first  squares,  a  distance  of  one-third  the  space  between 
the  first  series  of  squares.  Proceed  with  the  construc- 
tion of  the  spiral  following  consecutive  radii. 

The  second  method  is  practically  the  same  as  the 
first,  just  described.  The  radii  of  the  first  quadrants, 
both  inner  and  outer,  are  taken  on  the  line  CD.  Fojlow 
the  unbroken  lines  until  the  spiral  is  completed.  *The 
construction  of  the  diagonal  in  beginning  this  method 
is  the  same  as  in  Fig.  52.  The  offset  diagonal  is  equal 
to  one  of  the  smaller  spaces'  on  the  diagonal. 

Exercise  51. — Draw  a  i-inch  bolt  of  3  inches  length. 
There  are  8  threads  per  inch.  The  angle  of  the  V's 
in  the  U.  S.  Standard  or  Sellers  thread  is  60°.  Note 
the  difference  between  a  single  and  double  V  thread  in 


MECHANICAL  DRAWING  57 

the  conventional  layout.  A  square  has  half  as  many 
threads  as  a  V  of  the  same  diameter.  Show  length  of 
bolt  from  underneath  edge  of  head  to  the  end  of  the 
cylinder.  Figs.  55  and  88. 

Ornamental  and  decorative  art  implies  the  use  of 
geometry  in  laying  out  designs  and  patterns  in  stained 
or  art  glass,  carpets,  wall-paper,  oil-cloth,  borders, 
ornamental  iron,  woodwork  and  carving,  carpentry  and 
cabinetmaking,  pottery,  china  painting,  floor-tiling,  and 
in  bookbinding.  Meyer,  in  his  "Handbook  of  Orna- 
ment," says :  "In  medieval  times  these  geometric  con- 
structions developed  into  practical  artistic  forms  as 
we  now  see  them  in  Moorish  paneled  ceilings  and 
Gothic  tracery."  In  the  exhibit  of  Indian  relics  in  the 
Field  Museum  one  may  also  see  traces  of  geometric 
design  in  the  tattoo  and  decoration  of  the  imple- 
ments of  the  savage.  The  history  of  some  of  these  de- 
signs is  very  interesting,  particularly  the  Swastika  and 
the  Maltese  cross. 

Geometric  motives  may  be  obtained  from  the  flowers. 
The  trilium,  daisy,  columbine  and  lilac  are  illustrations 
of  the  triangle,  circle  and  polygon.  These  may  be  ar- 
ranged into  rosettes,  borders  and  stencils,  using  a  cir- 
cle as  a  unit. 

The  illustration  of  the  trefoil,  Fig.  32,  is  a  design 
of  a  monogram  of  an  appropriate  initial. 

Problems  pertaining  to  decorative  design  will  not 
be  given  in  this  course,  but  will  be  reserved  for  a  later 
work. 


CHAPTER  IV 

WORKING  DRAWINGS 

Tj^LSEWHERE  reference  has  been  made  to  the 
•*— '  value  and  importance  of  a  working  drawing  in 
the  shops.  No  reliable  workman  should  attempt  a  new 
problem  without  a  working  drawing  having  previously 


,     Fig.  56 


been  made.  No  first-class  foreman  should  permit  any 
other  kind  of  a  workman  to  begin  a  responsible  task 
without  having  ample  directions  in  plan  and  elevation. 
By  a  "plan"  is  meant  the  appearance  of  the  top  of 
an  object  when  observed  from  above.  By  "elevation" 


MECHANICAL  DRAWING 


59 


Fie.  57 


Fig.  58 


60  A  PRACTICAL  COURSE  IN 

is  meant  the  appearance  of  the  object  when  observed 
from  the  front  or  side.  Having  three  views  of  the 
object,  any  ordinary  problem  in  the  shops  may  be  made 
clear.  Occasionally  a  very  irregular  object  requires 
special  views,  but  for  our  immediate  purpose  these  will 
be  omitted. 

Suppose  a  model  be  placed  within  a  glass  case  and 
a  plan  view  traced  on  the  upper  surface.  Likewise 
trace  a  view  of  the  front  and  side.  Now  open  each 
plane  until  top,  front  and  side  lie  in  one  flat  surface 
as  in  Fig.  56.  This  is  the  working  drawing,  or  three 
projected  views.  Both  H  and  P  planes  revolve  through 
90°.  Note  the  references  to  height  (H),  width  (W), 
and  depth  (D),  together  with  the  method  of  obtaining 
them  from  one  view  and  carrying  to  another,  in  Fig. 
57- 

If  a  glass  case  with  hinged  sides  is  not  conveniently 
acquired  select  and  invert  a  good  pasteboard  shoe-box 
over  any  geometric  model.  Sever  all  but  the  front 
edges,  which  are  to  serve  as  hinges.  Outline  on  the 
surfaces  the  shape  of  the  several  views  and  then  cut 
out  the  outline  from  the  H,  V  and  P  planes.  A  chalk- 
box,  pencil-box,  prism,  or  any  object  which  is  simple 
in  shape,  will  serve  well  as  a  drawing  exercise.  Many 
problems  should  be  drawn  to  firmly  fix  the  funda- 
mental principles  of  projection  which  underly  the 
working  drawing.  While  the  geometric  exercises  form 
the  basis  of  all  mechanical  drawing,  the  details  and 
principles  of  the  workman's  drawing  are  the  most 
used  and  practical  application  of  constructive  drawing. 

The  craftsman,  patternmaker,  machinist  or  carpen- 
ter must  each  have  a  definite  plan  or  idea  prescribed 
before  him  in  the  form  of  a  blueprint  working  drawing. 
The  first  thought  of  any  constructive  character  must 


MECHANICAL  DRAWING  61 


Fie  59. 


63  A  PRACTICAL  COURSE  IN 

always  first  appear  on  paper,  and  the  common  means 
of  that  representation  is  the  above-described  kind  of 
drawing.  Fig.  58. 

PROBLEMS 

1.  Draw  three  views  of  the  rectangular  prism.  Fig. 
59- 

2.  Draw  three  views  of  the  pentagonal  plinth.  Fig. 
60. 

3.  Draw  two  views  of  the  bushing  pattern.  Fig.  61. 

4.  Fig.   62   is  a   representation   of   an   angle   iron. 
Draw  three  views  and  dimensions. 

5.  Fig.  63  is  a  drawing  of  a  cast-iron  block.    Two 
views  and  dimensions. 

6.  Fig.  64,  pillow-block  bearing.     Three  views  and 
dimensions. 

7.  Fig.  65,  tool  post  holder.     Three  views  and  di- 
mensions.    Scale  half  size.     Opening  of  slot  4^-in. 
long. 

8.  Fig.  66,  rocker.    Three  views  and  dimensions. 

9.  Fig.  67,  crank  arm.    Two  views  and  dimensions. 

10.  Fig.  68,  core  box  for  pipe  tee.    Three  views  and 
dimensions. 

11.  Fig.  69,  coupling.    Two  views  and  dimensions. 

12.  Fig.  70,  V  block.    Three  views  and  dimensions. 

13.  Fig.  71,  drawing  of  a  pattern  for  a  shaft  bear- 
ing without  the  cap.     Draw  three  views. 


MECHANICAL  DRAWING 


63 


Fie  61 


MECHANICAL  DRAWING 


Fie-  64 


A  PRACTICAL  COURSE  IN 


Fig  .6" 


MECHANICAL  DRAWING  67 


A  PRACTICAL  COURSE  IN 


Fig.  69 


•i— 

r    X 


Fie.  70 


MECHANICAL  DRAWING  69 


CHAPTER  V 

CONVENTIONS  USED  IN  DRAFTING 

/CONVENTIONS,  as  explained  in  a  previous  chap- 
^  ter  are  customary  methods  or  symbols  established 
by  usage  and  precedent  and  are  generally  employed  for 
the  sake  of  uniformity  and  convenience  the  world  over. 
Their  use  and  convenience  will  be  readily  understood 
by  the  student. 

a.  Circles  require  two  center  lines,  and  must  al- 
ways be  shown. 

b.  Invisible  edges  are  shown  by  a  series  of  ^-inch 
dashes  with  i/i 6-inch  space. 

c.  Visible  edge  lines  take  precedence  over  invisible 
lines  when  they  coincide. 

d.  Dimension  lines  are  very  light,  continuous,  and 
broken  only  for  dimensions,  near  the  center. 

e.  Dimensions  should  read  at  right  angles  to  the 
dimension  lines  in  the  working  drawing. 

/.  Sharp,  snappy  arrow-heads  should  attach  to  the 
ends  of  each  dimension  line. 

g.  The  summation,  or  aggregate  of  several  dimen- 
sions tending  in  any  one  direction,  should  be  shown 
separately,  that  the  workman  may  not  err  in  calculat- 
ing the  over-all  sizes  of  stock  required  for  the  finished 
product. 

h.  Projection  lines  are  light  single  dashes  of 
any  desirable  length  extending  from  view  to  view 
to  facilitate  the  placing  of  the  dimensions.  They  should 
not  touch  the  projections  of  the  figure. 

i.     Space  too  small  for  dimensions  should  have  ar- 


MECHANICAL  DRAWING  71 

rows  outside  and  directing  toward  the  space  to  be 
dimensioned. 

j.  The  draftsman's  figures  are  to  be  used  for  all 
numerals,  or  fractions,  which  must  be  common  shop 
units,  as  -5%,  T\,  f,  f,  etc.,  and  not  -j,  ^, 
TO>  iV  The  bar  which  separates  the  numerator 
from  the  denominator  should  always  be  horizontal  to 
avoid  any  possible  mistake  in  reading  a  dimension. 

k.  Section  planes  have  the  same  convention  as  cen- 
ter lines. 

/.  All  edges  of  material  which  are  shown  cut  by 
a  plane  in  the  drawing,  are  solid  lines. 

m.  Adjacent  pieces  in  an  assembly  of  parts  must 
be  crosshatched  at  right  angles,  or  in  different  direc- 
tions. Do  not  space  too  closely. 

n.  Dimensions  are  not  so  likely  to  be  overlooked 
by  the  workman  if  placed  to  the  right  and  between 
the  views  as  much  as  possible. 

o.  Do  not  permit  dimension  lines  to  cross  each 
other. 

p.  Show  dimensions  between  center  lines  and  "fin- 
ished" surfaces.  They  are  most  important  in  any 
drawing. 

q.  Sections  are  shown  to  make  clear  hidden  details 
of  construction.  They  should  be  frequent  and  prop- 
erly located  in  complex  drawings. 

r.  Do  not  repeat  dimensions  except  in  a  very  com- 
plicated drawing. 

s.  Always  place  full-size  dimensions  on  the  draw- 
ing, no  matter  what  scale  is  used. 

t.     Locate  the  "front"  elevation  first. 

u.     Invisible  parts  behind  sections  are  never  shown. 


72  A  PRACTICAL  COURSE  IN 

v.  Bolts,  shafts  and  screws  are  never  sectioned. 
A  broken  cross-section  of  a  bolt  or  shaft  should  show 
the  convention  of  material. 

w*     Show  diameters  in  preference  to  radii. 

x.     Never  cross-hatch  over  dimensions. 

y.  Arcs  of  circles  and  curves  should  be  drawn  be- 
fore straight  lines  which  adjoin  them. 

LETTERING 

One  of  the  most  important  features  of  any  draw- 
ing, and  one  most  neglected  on  the  part  of  a  student 
or  amateur  draftsman,  is  the  neat  appearance  of  every 
detail.  These  details  consist  chiefly  of  letters,  figures, 
notes,  titles,  scales,  stock  lists  and  bills  of  materials 
• — data  which,  if  executed  neatly  and  with  precision, 
increase  the  appearance  a  hundred-fold  of  what  might 
otherwise  be  a  poor  drawing. 

Architectural  and  mechanical  draftsmen  are  obliged 
to  letter  well  to  retain  their  positions  in  many  concerns 
although  they  may  be  expert  in  draftsmanship.  Com- 
petitive and  Patent  Office  drawings  must,  of  necessity, 
look  neat  in  every  particular  in  order  to  receive  a  con- 
sideration of  merit.  This  is  why  technical  schools 
insist,  with  emphasis,  upon  this  additional  good  quality 
of  their  student's  work. 

Notebooks,  examination  papers,  programs  and 
themes  appear  much  better  when  their  titles  are  well 
lettered  than  when  scribbled  in  some  unreadable  char- 
acters. 

NOTE  TO  THE  TEACHER  :  A  better  impression  of  a  student  is 
derived  from  the  manner  in  which  he  presents  his  work,  than 
from  how  much  work  he  presents.  Insist  that  what  he  does 
be  done  well,  and  what  he  lacks  in  quantity  will  be  more  than 
made  up  in  quality. 

If  cross-sectioned  paper  is  not  available,  it  will  be 


MECHANICAL  DRAWING  73 

THE    FOLLOWING  IS  A    GOOD    EXERCISE 
AND    CONTAINS    ALL      THE   LETTERS    OF 
THE    ALPHABET. •- 

"THE    QUICK   BROWN   FOX    JUMPS    OVER 
THE    LAZY   DOG." 

HARD    PRACTICE    IS    A     GOOD    MASTER. 

THE  DRAFTSMAN'S  FIGURES  ARE  AL- 

WA  YS    USED.   123456  7  Q  9  O  /  /j" 

ALL     LETTERS    AND    FIGURES     SLOPE 
HALF     THEIR    HEIGHT,     OR    ABOUT    30? 

Fig.  72 


This  lower  case   style  is   a  very 
popular   form  of  letters  for  notes, 
titles,  stock-lists,  bills   of  moterid,  etc. 

*A    quick  brown  fox  Jumps  over 
the  lazy   dog" 

Stem  fetters   are  ,%ths   of  an  inch 
high.  Use  a  ball-pointed  pen   *506  or 


Fig.  73 


A  PRACTICAL  COURSE  IN 


well  to  "rule"  a  sheet  into  ^-inch  squares  and  draw 
"slope"  lines  about  30°  from  a  vertical,  as  in  Fig.  73. 
Pencil  all  letters  freehand  for  guides,  with  a  2H 
pencil,  and  submit  for  approval.  ( Note :  Do  not  mis- 
take a  No.  2  pencil  for  a  2H.  Any  good  stationer  will 
explain  the  grading  of  pencils.)  Ink  with  Higgins' 
India  ink  and  ball-pointed  pen,  No.  506,  or  516. 

Fig.  72  is  an  exercise  which  contains  all  the  letters 
of  the  alphabet.    Some  such  sentence  as  this  is  usually 


TITLE 


NAME     OF    SCHOOL- 
SCALE,  DATE, 
PLATE    NO.,  NAME 


Vfe 


Fig.  74 

given  in  commercial  schools  to  develop  skill  on  the 
typewriter.  Lower-case  or  srriall  letters  are  shown  in 
Fig  73.  "Lower-case"  is  a  printers'  term,  printers' 
type  cases  being  so  arranged  that  the  capital  letters 
are  contained  in  the  upper  and  the  small  letters  in  the 
lower  compartments.  In  Fig.  74,  a  title  is  shown. 
Note  that  the  most  important  part  of  the  title  is  the 
object  of  the  drawing  and  hence  should  be  more  prom- 
inent than  the  rest.  A  title  should  be  so  balanced  that 
one  side  will  not  appear  to  "see-saw"  or  be  heavier 
than  the  other.  All  drawings  should  be  titled  prop- 


MECHANICAL  DRAWING  75 


TH/S   FREEHAND    GOTHIC   STYLE   OF 
LETTERS   SHOULD   BE  USED   ON  ALL 
DRAWINGS    NOT  ARCHITECTURAL    OR 
TOPOGRAPHICAL. 

MAKE  ALL    LETTERS    UNIFORMLY 
HIGH,  ^TH   INCH  IF   LOWER    CASE 
AND  ^TH  IF   CAPS.    THIS   STYLE  IS 
£TH   CAPS, 

DRAW   LIGHT    GUIDE  LINES    FOR 
THE  SLOPE  AND  HEIGHT    WIDE  LET- 
TERS   ARE  BEST   SPACE  BETWEEN 
WORDS  SHOULD   NOT  BE  LESS    THAN 
^TH  INCH,  NOR  MORE   THAN  JTHS. 
KEEP  LETTERS  IN  EACH  WORD   COMPACT 

GOOD    LETTERING   ENHANCES    THE 
APPEARANCE    OF   ANY   DRAWING. 

NEATNESS  AND  LEGIBILITY   ARE 
VALUABLE   ASSETS    IN   MECHANICAL 

DRAWING. 

QQ     NOT    USE    A     VERTICAL      STYLE. 

Fie.  75 


76  MECHANICAL  DRAWING 

erly.  The  titles  need  not  be  circumscribed  by  a  2x3^2- 
inch  boundary,  but  the  proportion  of  the  spacing  be- 
tween lines  and  heights  should  remain  as  in  the  illus- 
tration. Place  the  title  plate  in  the  lower  right-hand 
corner,  about  ^  inch  from  the  margin  line. 


aabcdefghv|klmnopc[rs-t 
uvwxyz 


UVWDCl/ 


Fig.  76 

Oval  letters  and  figures  are  constructed  on  the  form 
of  the  letter  "O."  Make  the  letter  "O"  and  then 
modify  to  suit  the  shape  of  the  desired  letter  or  figure. 

Draw  all  downward  strokes  first,  then  curves  or  in- 
tervening lines  as  indicated  in  Fig.  73. 

Practice  lettering  the  exercise  given  in  Fig.  75  until 
proficiency  is  assured. 

Fig.  76  is  an  architectural  style  of  letter. 


CHAPTER  VI 

MODIFIED   POSITIONS   OF  THE   OBJECT 

C  UPPOSE  the  prism  in  Fig.  59  (Page  61)  be  re- 
^  volved  about  a  vertical  axis,  i.  e.,  an  axis  1  (per- 
pendicular) to  the  H  plane.  Looking  down  on  the 
prism  in  Fig.  59,  how  would  the  plan  be  drawn  if  the 


object  be  revolved  30°  about  a  vertical  axis?  Does 
the  altitude  and  the  construction  of  the  plan  view  alter 
in  such  a  revolution?  Use  the  chalk-box  as  a  model 
until  each  step  in  the  thinking  process  is  clear.  Now 
draw  the  remaining  views.  Through  how  many  de- 


78 


A  PRACTICAL  COURSE  IN 


grees  does  the  earth  revolve  ?  May  anything  revolve  ? 
Any  point  of  the  object  always  moves  in  a  plane  1 
to  the  axis.  There  are  360  degrees  in  a  circle. 

Principle  i. — When  an  object  revolves  about  a  ver- 
tical axis  (1  to  H)  its  plan  view  is  not  altered  in  shape, 


but  only  in  position,  and  the  height  remains  the  same. 
Fig-  77- 

Note:  No  distinction  is  here  made  between  "ver- 
tical" and  "perpendicular,"  as  the  H  plane  is  always 
considered  horizontal. 


MECHANICAL  DRAWING  79 

Find  the  projections  of  the  plinth  in  Fig.  bo  (p.  61) 
when  it  is  revolved  through  an  angle  of  30°  about  a 
side  axis,  i.  e.,  //  (parallel)  to  the  profile  or  side  plane. 

The  observer  will  note  here  that  each  point  of  the 
object  revolves  in  a  circular  plane,  or  path,  through 
30°,  about  the  side  axis,  which  can  only  be  seen  as 
a  point  from  the  front.  Therefore,  the  front  elevation 
will  not  be  altered  in  construction  from  its  original  and 
natural  position,  but  its  position  will  be  30°  inclined 
to  the  base  upon  which  it  originally  lay.  Find  its  re- 
maining projections.  Looking  down  on  the  plinth  in 
Fig.  60,  as  on  the  prism,  when  it  is  revolved  about  a 
side  axis  (J_  to  V)  we  discover  that  the  depth  or  thick- 
ness does  not  alter,  but  the  construction  of  the  plan 
changes. 

Principle  2 — When  the  object  revolves  about  a  side 
axis  (1  to  V)  to  the  right  or  left,  its  front  elevation 
does  not  change,  save  its  position,  and  the  depth  (D) 
remains  the  same.  Fig.  78. 

Find  the  three  views  of  the  frustum  of  the  pyramid, 
Fig.  79,  when  it  is  revolved  through  an  angle  of  30°, 
forward  or  backward,  about  a  front  axis  (1  to  P). 

In  this  instance  we  must  first  observe  the  position  of 
the  object  from  the  profile  or  right-side  plane.  The 
revolution  about  the  front  axis,  which  may  be  seen 
as  a  line  parallel  to  the  ground  line,  GL,  and  pass- 
ing through  the  center  of  the  model,  is  then  accom- 
plished by  tilting  the  side  elevation  forward  or  back- 
ward, the  lower  edge  making  the  required  angle  with 
the  base  upon  which  the  object  stands.  Looking  down 
on  the  prism  in  Fig.  59,  again,  it  will  be  seen  that  the 
width  of  the  object  does  not  alter  when  it  is  revolved 
forward  or  backward.  Draw  the  three  projections 
when  so  revolved,  commencing  with  the  side,  then  the 


80 


MECHANICAL  DRAWING 


front,  and  the  plan  last.  In  this  case  all  points  of 
the  object  revolve  in  planes,  which  the  observer  can 
only  see  as  straight  lines  //  to  VL. 


Principle  3. — When  the  object  revolves  about  a  front 
axis  (1  to  P),  forward  or  backward,  its  side  elevation 
does  not  change  save  in  its  position,  and  the  width  re- 
mains the  same. 


CHAPTER  VII 

THE    DETAILED    WORKING    DRAWING 

A  MACHINE  is  a  composition  of  many  parts. 
•*""*•  Each  part  performs  a  certain  function  and  bears 
a  close  relation  to  adjacent  members.  If  a  mechanic 
desires  to  make  a  machine,  he  must  organize  the  parts 
perfectly  so  that  a  minimum  amount  of  friction  is  had 
to  do  the  required  work.  When  each  part  is  made  in 
the  shops  every  specific  detail  is  worked  out  separately. 
In  the  problem  of  the  connecting  rod,  every  detail  is 
illustrated  in  such  a  manner  that  it  will  be  very  easy 
to  imagine  the  size,  shape,  and  to  some  degree,  at  least, 
the  relative  position  of  the  parts  when  assembled  to- 
gether. The  connecting  rod  carries  the  power  direct 
from  the  cylinder  through  the  piston  to  the  drivers  of 
a  locomotive.  This  object  is  a  detail  of  a  stationary 
engine.  A  detailed  working  drawing  is  made  to  enable 
the  mechanic  to  construct  each  detail  without  con- 
fusion. 

From  the  illustrations  make  a  working  drawing  of 
each  separate  part,  and  then  fit  them  together  in  an 
assembly  drawing. 

Figs.  80  and  81  are  parts  of  a  bearing  which  sur- 
round the  cross-head  pin  and  fit  in  the  left-hand  end 
of  the  rod,  Fig.  87.  Fig.  82  is  a  tapered  key-block  used 
to  take  up  wear  and  is  located  behind  Fig.  80.  Figs.  83 
and  84  are  parts  of  the  bearing  which  fit  around  the 
crank-pin  and  are  located  on  the  right  end  of  the 
rod,  Fig.  87.  A  strap,  Fig.  85,  holds  these  two  parts 
together  with  another  tapered  key-block,  Fig.  86,  by 
means  of  half-inch  bolts.  Two  J^-in.  bolts.  6  in.  long, 
Fig.  88,  fasten  the  strap  to  the  rod.  Each  tapered  key- 


A  PRACTICAL  COURSE  IN 


Fig.  80 


Fig-  81 


Fig.  82 


MECHANICAL  DRAWING 


83 


Fig.  83 


Fig.  84 


A  PRACTICAL  COURSE  IN 


V\ 


Fig.  85 


Fig.  86 


MECHANICAL  DRAWING  85 

block  has  two  ^-inch  bolts,  one  on  each  side  of  the 
strap.  This  makes  six  bolts  in  all.  The  hole  on  the 
end  of  the  strap  is  for  oil.  Copy  in  Gothic  slant  letters 
the  stock  list.  Fig.  89. 


Fig-  87 

When  the  drawing  of  a  machine  problem  is  com- 
pleted, it  is  first  sent  to  the  patternmaker,  who  makes 
a  model  in  wood  from  it.  He  must  know  from  ex- 
perience the  amount  of  material  to  allow  for  shrinkage 


Fig:.  88 


of  the  casting  in  cooling,  how  much  to  allow  for  polish- 
ing or  "finishing,"  and  how  much  taper  for  "draft"  in 
withdrawing  the  pattern  from  the  mold.  The  pattern 
is  then  sent  to  the  foundry,  where  it  is  molded  in  sand. 
After  the  form  has  been  made  it  is  "poured,"  that  is, 


A  PRACTICAL  COURSE  IN 


filled  with  melted  ore  from  the  cupola.    When  the  cast- 
ing is  cool  enough  to  handle,  it  is  sent  to  the  machine- 
shop  to  be  machined  and  "dressed"  ready  for  use. 
Here,  again,  the  working  drawing  must  be  brought 

STOCK  L/ST 


MARK 

NO. 
WANT 

NAME 

MATERIAL 

REMARKS. 

80-81 

/ 

BEARING 

PH.  BRONZE 

2  PARTS 

82 

/ 

KEY-BLOCK 

STEEL 

F.A.O. 

86 

/ 

„ 

" 

" 

83-84 

1 

BEARING 

PH.BRONZE 

FINISH 
BABBI  TT 

85 

/ 

STRAP 

STEEL 

F.A.O. 

87 

1 

ROD 

" 

" 

88 

E 

BOLTS 

W.I.    ' 

6"X/D 

1 

" 

" 

3"X/D 

2 

a 

H 

^"x/b 

1 

" 

// 

//'X/'D 

Fig.  89 

into  use,  for  the  machinist  is  obliged  to  follow  the 
specifications  thereon,  regardless  of  what  he  might 
think  ought  to  be  done  in  the  case.  This  places  all  the 
responsibility  of  error  upon  the  draftsman. 

A  detailed  working  drawing,  as  applied  to  the  wood- 
working and  building  trades,  is  also  a  very  important 
application  of  the  working  drawing.  It  is  fully  as 


MECHANICAL  DRAWING 


87 


Fie.  90 


necessary  that  such  a  drawing  be  as  carefully  made  for 
the  carpenter  or  cabinetmaker  as  for  the  machinist  or 
engineer,  and  no  skilled  workman  should  attempt  a 
task  requiring  skill  and  accuracy  without  it. 


88 


A  PRACTICAL  COURSE  IN 


For  erecting  the  framework  of  a  cottage,  details 
specific  and  clear  must  accompany  the  plans  and  eleva- 
tions. Studs,  sills,  rafters,  sashes,  joists,  etc.,  should 


Fie 


be  so  located  as  to  give  the  greatest  service.  Fig.  90 
shows  an  isometric  representation  of  a  framing  detail, 
and,  although  not  in  accordance  with  the  orthographic 
working  drawing,  shows  to  an  untrained  imagination 


MECHANICAL  DRAWING  89 

a  better  idea  of  the  construction.  Note  the  dimensions 
between  members,  size  of  stock  and  joinery.  The 
plate,  at  A,  for  the  second  floor,  is  usually  set  in  an 
inch  in  the  studding.  This  is  called  a  gained  joint. 


NEWEL  \ 

/=>OS7~6*6 


Fig.92 


Other  forms  of  joints  are  miter,  tongue-and-groove, 
tcnon-and-mortise  (C),  dovetail  (E),  half-end  lap  (D), 
bridge  (B),  butt  (F)  and  open  tenon  with  key,  each 
having  a  special  purpose  for  its  use.     Fig.  91. 
Problem  i. — Make  an  assembled  drawing — plan  and 


90  MECHANICAL  DRAWING 

front  elevation — of  the  framing  details  suggested  in 
Fig.  90,  and  dimension  properly.  Scale  il/2  inch  =  I 
foot. 

Problem  2. — As  in  Problem  i,  make  a  drawing  of 
the  stair  detail.  Risers,  7" ;  tread,  10"  wide.  Balus- 
ters 2"  square  and  space  equal  to  the  width  of  baluster. 
Fig.  92. 

Problem  5. — Make 'a  working  drawing  of  the  forms 
of  joints  used  in  joining  represented  in  the  illustration. 
Scale,  half-size.  Dimension.  Use  stock  sizes  of  ma- 
terials. Fig.  91. 

Problem  4. — Make  a  floor  plan  of  your  home, 
a  barn  or  school-room,  and  show  all  >  appointments. 
Scale  Y&"  to  the  foot.  Small  details  are  usually  drawn 
larger  or  to  full  scale. 

Problem  5. — An  examination  in  high-school  draw- 
ing included  the  following:  Make  to  scale  }4"  to  i' 
an  architect's  plan  for  the  upper  five-room  flat  in  a 
modern  three-story  building.  Show  by  the  customary 
architectural  conventions  all  that  is  necessary  and 
usual.  Outside  dimension  22'  6"x36'. 


CHAPTER  VIII 

PATTERN-WORKSHOP  DRAWINGS 

/"\  NE  of  the  most  useful  applications  of  the  working 
^^  drawing  is  the  laying  out  of  patterns,  or  devel- 
opments. The  theory  of  such  a  drawing  is  found  in 
the  study  of  Descriptive  Geometry — a  science  which 
all  architects  and  engineers  are  required  to  know  some- 
thing about  and  which  is  extremely  useful  to  drafts- 
men, although  often  avoided. 

A  thorough  knowledge  of  the  principles  of  pattern- 
making  enables  the  tinsmith  or  sheet-metal  worker  to 
lay  out  very  complicated  patterns  in  a  very  simple  geo- 
metric manner  and  thereby  save  time  and  material  to 
all  concerned.  Cutting  a  pattern  so  as  to  be  as  econ- 
omical as  possible,  requires  foresight  which  the  usual 
patternmaker  fails  to  exercise.  Tin-plate  scraps  often 
may  be  used  to  as  good  or  better  advantage  than  new 
sheets,  if  conservatively  and  thoughtfully  cut,  and  in 
all  kinds  of  work  stock  should  be  ordered  so  that  a 
minimum  amount  of  waste  is  left. 

A  pattern  is  a  plane  surface  representing  the  un- 
folded sides  of  an  object  equal  to  the  perimeter  of  its 
right  section,  the  width  equal  to  the  altitude  of  the 
object,  or,  rather,  the  true  length  of  its  lateral  surface. 

Develop  the  surface  of  a  cylinder  or  prism  upon  a 
sheet  of  bristol  paper,  allowing  ft  inch  for  lap.  Glue 
the  lap  and  fasten  together  for  a  facsimile  of  the  orig- 
inal. Add  bottom  and  top. 

In  most  cases,  in  beginning  a  problem,  it  is  only  nec- 
essary to  draw  the  plan  and  front  elevation  plus  an 
auxiliary  sectional  view  to  show  the  true  size  of  the  cut 
section.  From  any  of  the  illustrations,  Figs.  93  and 


MECHANICAL  DRAWING  93 

95,  it  will  be  seen  that  the  object  is  projected  up  into 
the  plane  of  the  paper  to  obtain  the  auxiliary  view. 
After  the  pattern  is  drawn  it  is  transferred  from  the 


manila  or  bristol  paper  to  the  metal  by  pricking  points 
with  a  sharp  punch  along  the  contour  of  the  pattern, 
due  allowance  being  made  for  lap  and  seam.  The 
double  edge  shown  on  the  development  of  the  quart 
measure  is  for  the  lock  seam  shown  at  A,  Fig.  100. 


94  A  PRACTICAL  COURSE  IN 

PARALLEL   METHOD 

Problem  I. — A  truncated  hexagonal  prism  is  to  be 
developed  as  shown  in  Figs.  93  and  94.  Use  any  suit- 
able dimensions.  Construction :  Draw  the  plan  and 


Fig.  96 

elevation,  also  sectional  view,  as  at  A.  The  width  of 
the  section  and  base  is  the  same  as  the  depth  of  the 
prism  transferred  from  the  plan  view.  In  the  "layout" 
the  various  heights  of  the  linear  elements  of  the  prism 
are  laid  off  on  corresponding  parallels  in  a  straight  line, 
equal  in  length  to  the  perimeter  of  the  base. 

Problem  2. — A  truncated  hexagonal  pyramid  is  to  be 
developed,  as  shown  in  Figs.  95  and  96,  to  suitable 


MECHANICAL  DRAWING 


Fig.  97 


Fig.  99 


Fig.  98 


06 


A  PRACTICAL  COURSE  IN 


dimensions.  Construction :  Obtain  the  projections 
and  sectional  view  as  in  Problem  i.  To  obtain  tbe 
development  it  is  necessary  to  know  the  slant  height 
of  the  pyramid.  The  exterior  edges  are  parallel  to  the 
vertical  plane;  therefore,  their  true  lengths  must  be 
seen  at  AC.  With  a  compass  set  with  AC  as  a  radius. 


describe  an  arc.  Lay  off  the  perimeter  of  the  base  on 
this  arc  and  join  all  points  with  radial  lines  to  the 
center  of  the  arc  C.  Step  off  the  true  length  of  each 
cut  element,  o,  i,  2,  3,  shown  projected  on  AC;  then 
join  as  in  Fig.  96.  To  complete  the  pattern  add  the 
section  and  the  base. 

Problem  3. — Develop  a  frustum  of  a  rectangular 
pyramid,  base  2"xi^4"  and  altitude  3". 

Problem  4. — An  irregular  cone  is  projected  in  Fig. 
97.  Develop  by  radial  lines  as  in  Fig.  96,  except  that 
the  true  length  of  each  element  be  found  separately. 


MECHANICAL  DRAWING  97 

Problem  5.  —  Given  the  front  elevation  of  a  1^2" 
cylinder,  Fig.  98,  draw  the  plan  and  develop. 

Problem  6.  —  Draw  the  pattern  of  a  quart  measure, 
Figs.  99  and  100,  diameter  of  upper  base  3",  lower  5". 
Find  the  altitude.  Note:  This  problem  involves  a 
principle  of  mensuration.  Use  either  dry  or  liquid 
measure. 

V  V 

-   —  A,   or  -  —  A, 

rR*  D2   (.7854) 

where  V  =  the  volume,  or  solid  contents  and  A  = 
the  altitude.  This  is  approximate.  To  be  exact,  the 
formula  should  be  stated  as  follows  : 


b  +  <~^~~  •     =  V, 


when  a  =.  area  of  upper  base. 
b  —  area  of  lower  base. 
h  =  height  or  altitude. 

There  are  231  cubic  inches  in  a  liquid  gallon  and 
2150.42  cubic  inches  in  a  bushel. 

The  problem  here  indicated  is  one  of  finding  the 
altitude  of  the  frustum  of  a  cone.  Substitute  the 
known  value  of  V,  the  volume,  and  solve  for  h  as  in 
any  equation. 

Fashion  a  suitable  strip  for  a  handle  allowing  ffl' 
lap  for  edges.  The  illustration,  E,  Fig.  99,  shows  the 
lap  over  a  wire  at  the  top  of  the  cup.  A  customary 
rule  for  lap  is  4  X  thickness  of  metal  -f-  twice  the 
diameter  of  wire. 

Problem  7.  —  An  irregular  triangular  pyramid  having 
an  altitude  of  4>^",  the  sides  of  its  base  2"  or  more 
in  length  and  all  lateral  edges  oblique  to  all  planes 
of  projection,  has  two  lateral  edges  and  base  cut  by  a 


98  A  PRACTICAL  COURSE  IN 

sectional  plane  perpendicular  to  V  and  oblique  to  H. 
Draw  the  three  orthographic  views  and  the  true  size 
of  the  section.  Develop.  Figs.  101  and  102. 

Problem  8. — An  irregular  oblique  quadrilateral 
prism  has  a  right  section  resembling  Fig.  103.  Use 
suitable  dimensions.  Its  axis  is  inclined  30°  to  the 
right  of  its  base,  which  is  horizontal.  A  plane  inclined 
60°  to  the  left  of  its  base  cuts  all  the  lateral  edges  of 
the  prism.  Draw  the  three  projections  and  the  auxil- 
iary or  sectional  view.  Develop,  adding  the  base  and 
sectional  view. 

Problem,  p. — Draw  three  views  of  a  regular  vertical 
pentagonal  pyramid,  with  apex  above  the  base.  The 
rear  edge  of  the  base  is  inclined  15°  to  the  vertical 
plane  of  projection,  V,  the  left  end  of  this  edge  to  be 
nearest  V.  The  diameter  of  the  circumscribing  circle 
of  the  base  is  2"  and  altitude  4".  The  pyramid  is  cut 
by  a  plane  perpendicular  to  V  and  at  an  angle  of  60° 
to  its  base.  Show  the  line  of  intersection  in  three 
views,  make  a  sectional  view,  and  develop  either  trun- 
cated part. 

Problem  10. — A  circular  ventilator  projects,  through 
a  gambrel  roof  as  shown  in  Fig.  104.  Work  out  the 
line  of  its  penetration  with  the  roof  planes.  Develop 
the  ventilator  top  and  also  the  roof  planes,  showing 
the  line  of  penetration.  Scale  i"  =  i'  o". 

Problem  n. — Develop  a  truncated  right  cone  from 
the  illustration.  Fig.  105. 

Note :  Problems  7,  8,  9  and  10  are  intended  as 
test  problems. 

Any  development  of  a  geometric  form  is  a  mathe- 
matical process,  and  hence  should  receive  some  such 
consideration. 


MECHANICAL  DRAWING 


Fie-  101 


fie  102 


100  A  PRACTICAL  COURSE  IN 

The  following  formulas  are  self-evident  and  should 
be  committed  to  memory: 

2?rR  =  the  circumference  of  a  circle. 

TrR2  =  area  of  a  circle. 

(7rR2)L  =  volume  of  a  cylinder  when  L  altitude. 

(27rR)L  =  lateral  surface  of  cylinder. 

(7rR2)L/3  =  volume  of  cone. 

(27rR)S/2=:  lateral  surface  of  a  cone  when  S  — 
slant  height. 

6(XY/2)  =  area  of  a  hexagon  when  X  =  one  side 
of  the  polygon  and  Y  =  the  apothem. 

Note:  The  apothem  of  a  polygon  is  the  perpendicu- 
lar distance  from  the  center  of  a  polygon  to  one  of  its 
sides. 

6(XY/2)L  =  volume  of  a  hexagonal  prism. 

6 (XL)  =  lateral  surface  of  a  hexagonal  prism. 

(2TR)D  =  lateral  surface  of  a  sphere  when  D  = 
diameter. 

Problem  12. — Develop  a  cylinder  when  R=24", 
L  =  3". 

Problem  13. — Develop  a  cone  when  R  is  given  and 
the  volume. 

Problem  14. — The  area  of  an  octagon  is  24  square 
inches.  X  =  fy".  Develop  full  size. 

Problem  15. — Y  =  y2",  L  =  2y2".     Develop. 

Note :  This  problem  involves  a  geometfic  construc- 
tion of  a  hexagon  without  a  circle  before  a  develop- 
ment can  be  m^de.  Using  different  data,  originate 
and  solve  other  problems. 

Problem  16. — Fig.  106  shows  the  form  of  a  sheet- 
metal  hood  for  a  forge.  Scale,  half  size. 


MECHANICAL  DRAWING  101 

-2-6— 


Fig. 105 


103 


® 


® 


104  A  PRACTICAL  COURSE  IN 

Problem  17. — Fig.  107  gives  the  front  elevation  of 
of  6"  stove  pipe  elbow,  and  Fig.  108  the  development 
of  a  large  and  small  section. 

Problem  18. — Develop  a  3"  sphere  by  the  "orange 
peel"  method.  Fig.  109. 


Fie.  109 


Problem  ip — Secure  a  good  model  of  a  funnel  and 
draw  out  the  pattern. 


METHOD   OF  TRIANGLES 


Problem  20. — Tapering  ventilator  collar.  Many 
problems  are  impossible  to  develop  by  either  method 
previously  referred  to,  on  account  of  their  surfaces 
being  warped.  A  warped  surface  cannot  be  laid  out 


MECHANICAL  DRAWING 


105 


geometrically,  but  it  can  be  constructed  approximately 
by  means  of  triangles.  The  mold-board  of  a  plow, 
"cowcatcher"  of  a  locomotive,  marine  ventilator  fun- 
nels, grain  elevator  spouts,  a  cow's  horn,  stacks,  coal 


Fie.  no 


106  A  PRACTICAL  COURSE  IN 

scuttles,  footballs,  and  similar  objects  with  irregular 
surfaces,  are  non-developable  except  by  the  approxi- 
mate method  above  referred  to.  Construction:  Lay 
off  on  the  projections  of  the  figure  small  triangles  at 
regular  intervals,  determine  their  true  size  and  lay  ad- 


Fig,  in 

jacent  to  each  other.  This  will  constitute,  as  near  as 
may  be  done,  a  working  pattern.  The  base  of  each 
triangle  is  shown  in  the  plan  view,  the  altitude  in  the 
elevation.  Fig.  no. 

The  hypotenuse  of  any  right-angle  triangle  is  easily 
determined  when  two  of  its  sides  are  known.  Devel- 
opment (Fig.  in)  :  Lay  off  at  any  convenient  place 
a  radial,  and  for  our  purpose  we  will  select  the  long- 
est. At  the  lower  end  strike  an  arc  equal  to  X-2  on 
the  sectional  view  of  the  roof  plane.  With  center  at 
2',  Fig.  in,  and  radius  equal  to  the  length  of  the  first 
diagonal  1-2",  intersect  the  small  arc  1-2".  Small 
arcs  are  equal  to  C-D.  With  center  2"  and  radius 
1-3  strike  arc  at  X,  then  lay  off  second  radial  on 
either  side  of  first  radial,  1-2'.  Repeat  until  all  radials 
and  diagonals  have  been  used.  Any  warp  surface 
may  be  developed  in  this  manner. 


MECHANICAL  DRAWING  107 


108 


A  PRACTICAL  COURSE  IN 


Problem  21. — Select  a  kitchen  utensil  which  pri- 
marily must  be  laid  out  in  pattern  and  make  a  develop- 
ment to  scale.  A  dust-pan,  roasting-pan,  coffee-urn, 
colander  or  coal  scuttle  is  suggested.  Use  any  method 


Fig.  113 

or  combination  of  methods,  but  be  sure  to  determine 
whether  the  surface  can  be  developed,  or  is  warped, 
or  any  part  thereof.  Develop  a  truncated,  irregular 
cone,  Fig.  97  (page  95),  by  triangles. 

DEVELOPMENT  BY  REVOLUTION. 

Fig.  112.  This  method  is  not  so  practical,  but  is 
more  mathematically  exact  than  former  methods  re- 
ferred to  and  is  especially  used  to  verify  the  radial 


MECHANICAL  DRAWING  109 

line  method.  In  geometry  we  are  told  that  a  point 
revolves  about  an  axis  in  a  plane  perpendicular  to 
the  axis.  This  holds  true  here,  for  the  upper  edges  of 
the  truncated  section  revolve  in  perpendicular  paths  to 
the  lower  edge  of  the  base.  The  length  of  the  radius 
of  revolution  is  determined  by  constructing  a. right- 
angle  triangle  one  side  of  which  always  equals  the  dis- 
tance AX  from  the  horizontal  projection  of  the  point 
A  to  the  axis  1-2  in  the  plan, — the  other  of  the  per- 
pendicular altitude,  A'-D',  from  the  vertical  pro- 
jection to  the  plane  of  the  base.  The  hypotenuse  must 
equal  RX.  Connect  i-R,  which  is  the  true  length  of 
i -A.  This  interesting  exercise  should  be  repeated 
until  every  step  is  clear.  It  is  a  graphical  explanation 
of  the  same  process  in  mensuration. 

A  second  method,  and  closely  related  to  the  above, 
is  to  find  the  true  length  of  each  edge  of  the  truncated 
pyramid  and  lay  off  these  true  lengths  on  the  paths  of 
revolution  as  drawn  through  the  upper  points  A.  E,  F, 
G,  etc.,  from  points  of  the  base  X,  to  R.  The  method 
of  finding  the  true  length  of  i'-A'  is  shown  by  re- 
volving i -A  parallel  to  GL  and  projecting  to  the 
base  of  the  pyramid  i',  then  moving  to  its  revolved 
position  and  A'  also.  The  true  length  of  i'-A'  is  now 
shown  at  i"-A".  Fig.  113  is  an  isometric  illustra- 
tion of  the  above. 


CHAPTER  IX 

PENETRATIONS 

TT7HEN  one  object  intersects  or  penetrates  an- 
*  ^  other,  the  line  of  intersection  of  the  two  is 
denned  where  they  meet.  To  determine  the  pattern 
this  line  must  always  be  geometrically  located,  as  in 
Fig.  114,  and  herein  lies,  very  frequently,  a  difficult 
problem  if  the  subject  of  working  drawings  and  pro- 
jections has  not  been  thoroughly  mastered. 


MECHANICAL  DRAWING 


111 


DEVELOPMENT    BY    PARALLEL    PLANES 

Problem  i. — Fig.  114  is  an  illustration  of  two  inter- 
secting- pipes.  First,  draw  the  plan  and  front  eleva- 
tion. Conceive  a  series  of  parallel  planes,  A,  B,  C,  D, 
E,  F,  G,  cutting  through  both  pipes  and  parallel  to 


Fig.  US 

the  front  elevation.  Each  plane  cuts  two  elements 
from  each  pipe,  and  all  of  the  four  elements  lie  in 
the  same  plane.  In  this  case,  two  elements  of  pipe  B 
penetrate  one  element  of  pipe  A.  Determine  the  pro- 
jections of  each  element  thus  cut,  and  where  they 
intersect  is  a  point  of  penetration. 

To  develop  either  A  or  B,  lay  out  the  perimeter  of 
a  right  section,  the  height  of  the  pattern  being  equiva- 


112  A  PRACTICAL  COURSE  IN 

lent  to  the  length  of  the  elements  from  the  end  of  the 
cylinder  to  the  line  of  penetration. 

A  right,  sectional  view  shows  the  shortest  possible 
circumference  or  perimeter  of  the  object  and  is  deter- 
mined by  a  plane  perpendicular  to  the  axis  of  the 
figure. 

Problem  2. — Fig.  115  represents  a  small  rhombic 
prism  penetrating  a  larger  one,  the  top  of  each  being 
a  square  in  plan.  Establish  the  lines  of  penetration  in 
both  plan  and  elevation,  lay  out  the  development  of 
the  smaller  prism  and  develop  the  hole  in  the  larger. 
Locate  the  line  of  penetration  in  the  development  of 
the  smaller  prism.  A,  B,  C,  D  are  planes  passed 
parallel  to  the  vertical  plane.  Find  the  projections  of 
each  element  cut  from  both  prisms.  Where  they  meet, 
or  intersect,  determines  the  line  of  penetration,  for 
each  cut  element  lies  in  the  same  auxiliary  plane.  Num- 
ber each  point,  or  letter  with  some  familiar  symbol. 
When  objects  are  oblique  to  H  or  V  pass  a  plane  to 
determine  the  true  perimeter  of  the  right  section.  The 
trace  of  such  a  plane  in  this  problem  must  be  perpen- 
dicular to  the  lateral  edges  of  either  prism.  The  de- 
velopment must  be  made  from  this  sectional  line  and 
in  a  similar  manner  to  the  layout  of  the  hexagonal 
prism,  Problem  i,  Fig'.  94  (page  92). 

Problem  j. — As  in  problems  I  and  2,  find  the  line 
of  penetration  of  a  right  cylinder  with  a  right  cone. 
Fig.  1 1 6.  Pass  horizontal  planes.  Axes  of  both  fig- 
ures lie  in  the  same  plane.  Use  appropriate  dimen- 
sions. Note  that  each  plane  cuts  a  circle  from  the 
cone  and  two  elements  from  the  cylinder.  This  is  an 
illustration  of  a  conical  hopper  connecting  with  a  cyl- 
indrical pipe,  or  a  gutter  drip  and  rain-water  pipe,  as 
seen  on  many  houses. 


MECHANICAL  DRAWING 


113 


Problem  4. — A  vertical  pyramid  4"  high,  with  a  tri- 
angular base,  length  of  one  side  2l/2" ',  one  edge  of  base 
making  15°  with  V,  is  penetrated  by  a  horizontal  equi- 
lateral triangular  prism,  4"  long  and  perimeter  of  6^". 
One  face  is  parallel  to  V  and  i"  from  the  vertical  axis 


Fig.  116 


114 


A  PRACTICAL  COURSE  IN 


of  the  pyramid.  The  axis  of  the  prism  is  ij^f"  above 
the  base.  Draw  three  views  full  size,  find  the  line  of 
penetration  and  develop  both  objects.  Figs.  117,  118 
and  119. 


7NE 


Fig.  117 

Problem  5. — A  conical  steeple  of  a  cylindrical  tower 
is  penetrated  by  the  roof  planes  of  a  hip  roof.  Fig. 
1 20.  Find  the  line  of  penetration  and  lay  out  the  de- 
velopments of  the  conical  roof  and  of  the  roof  plane 
adjacent  to  the  hip,  showing  the  lines  of  penetration 
therein.  Scale,  ft"  =  i'  o". 

After  drawing  the  plan  and  elevation  from  the  illus- 
tration, Fig.  120,  pass  planes  M,  N,  O  and  P  to 
determine  the  line  of  penetration.  As  each  plane  is  // 
to  the  base  of  the  cone  it  will  cut  a  true  circle  from  the 
cone,  as  shown  in  the  plan.  It  will  also  cut  a  line 


MECHANICAL  DRAWING 


115 


XM         S  V  K     Y 

Fie.  118 

from  each  roof  plane  parallel  to  the  base  of  the  hip 
roof.  Where  this  element  crosses  the  circle  cut  by  the 
same  plane  is  a  point  of  penetration.  A  series  of 
similarly  acquired  points  will  determine  the  line  of 
intersection. 

To  develop  a  roof  plane  revolve  the  point  O  of  the 
upper  corner  of  the  hip  into  the  same  plane  as  the  base 
of  the  cone  and  the  roof,  by  the  triangle  method.  O 


Fig.  119 


116 


A  PRACTICAL  COURSE  IN 


Fie.  120 


MECHANICAL  DRAWING 


117 


moves  in  a  plane  1  to  the  axis  XY.  Points  10,  1 1  and 
12  move  perpendicularly  to  the  roof  lines  drawn 
through  A,  B  and  C.  The  development  of  the  cone 
has  been  described.  Fig.  121. 


Fig.  121 

Problem  6. — Develop  the  pattern  for  the  base  of  a 
blower  from  dimensions  given  in  Figs.  122  and  123. 
The  right  and  left  sides  of  this  base  are  elliptical 
cylinders,  that  is,  are  not  circular  in  cross  section.  The 
true  size  of  the  cross  section  cut  by  plane  Tt'  is  shown 
at  X  in  the  plan.  This  is  the  line  of  development,  Tt', 
Fig.  123.  The  lengths  of  each  element  can  easily  be 
laid  out  and  the  triangular  faces  added.  Draw  to  suit- 
able scale. 

Problem  J. — Develop  the  slope  sheet  of  a  locomotive 


118 


A  PRACTICAL  COURSE  IN 


Fiff.  122 

as  given  in  Fig.  124,  one-half  to  be  developed  by 
triangulation.  This  is  one  of  several  practical  prob- 
lems to  be  derived  from  a  study  of  the  locomotive  for 
purposes  of  developments.  The  steam-dome,  sand- 
dome  and  smoke-stack  are  other  illustrations  of  right 
cylinders  penetrating  the  outside  cover  of  the  boiler 
and  requiring  templets  or  patterns. 


Fig.  123 


MECHANICAL  DRAWING 


119 


Problem  8. — Draw  the  front  elevation  of  the  tran- 
sition piece  and  develop  by  triangles  or  the  method  sug- 
gested. Fig.  125. 


Fig:.  124 


Problem  p. — A  regular  vertical  triangular  prism, 
with  a  perimeter  of  10^"  and  4"  altitude,  has  its  front 
face  inclined  backward  and  to  the  left  at  15°.  A  right 


120 


MECHANICAL  DRAWING 


square  prism  of  6y2"  perimeter  and  4"  altitude  pene- 
trates the  former.  Axes  of  both  solids  intersect  at 
their  center  points.  Develop  both  objects. 


Fig.  125 


CHAPTER  X 

ISOMETRIC   WORKING  DRAWING 

AN  ISOMETRIC  drawing  is  generally  conceded  to 
be  a  pictorial  or  perspective  representation,  and 
for  practical  purposes  it  has  come  to  be  eminently  use- 
ful to  the  artisan  in  clarifying  hidden  constructions. 
Among  draftsmen  it  has  supplemented  the  freehand 
perspective  sketch  on  account  of  the  comparative  ease 
with  which  the  picture  is  made  by  the  instruments. 

The  few  principles  of  isometric  drawing  may  briefly 
be  summed  up  as  follows : 

a.  All  vertical  edges  in  the  object  are  vertical  in  the 
drawing,  as  in  freehand. 

b.  All  horizontal  edges,  representing  right  angles 


122 


A  PRACTICAL  COURSE  IN 


orthographically,  make  30°  to  the  horizontal  in  the 
isometric  construction. 

c.  Non-isometric  lines  of  edges  making  other  than 
right  angles  must  be  laid  off  orthographically  first  and 
then  transferred  to  the  isometric  drawing.  This  dis- 
torts the  true  length  of  non-isometric  lines,  but  does 
not  mar  the  pictorial  effect. 


Fig.  127 

d.  Surfaces,  not  lying  in  the  same  plane,  are  estab- 
lished from  center-isometric  axes. 

e.  Isometric    circles    are   drawn    within    isometric 
squares   of   the   same   diameter   as   the   given   circle. 
Elliptic  or  irregular  curves  are  constructed  flat,  then 
transferred.    Fig.  126. 


MECHANICAL  DRAWING 


123 


124  A  PRACTICAL  COURSE  IN 

/.  Isometric  workshop  drawings  are  dimensioned. 
Dimensions  must  be  placed  parallel  to  the  isometric 
lines.  Fig.  127. 

g.  The  usual  custom  of  shading  an  isometric  draw- 
ing is  to  accent  the  edges  separating  light  surfaces  from 
dark,  assuming  the  light  to  come  from  the  left  at  an 
angle  of  45°.  A  better  method,  and  one  which  en- 
hances the  pictorial  effect,  is  to  shade  all  edges  which 
are  nearest  the  observer's  eye.  This  tends  to  lift  the 
drawing  of  the  object  from  the  paper  and  relieve  the 
unnatural  effect  of  the  isometric  construction.  Fig. 
127  is  an  illustration  of  the  stub  end  of  a  connecting 
rod  and  exemplifies  the  second  method  described  above. 
There  are  many  draftsmen,  however,  who  do  not  shade 
any  drawings.  The  true  purpose  of  shading  is  to 
make  the  drawing  more  attractive,  but  aside  from  this 
it  has  no  value. 

h.  Invisible  lines  are  seldom  shown  in  isometric 
drawings  except  where  irregular  lines  are  hidden  by 
regular  surfaces  and  the  information  desired  can  in  no 
other  way  be  shown. 

The  illustrations  in  the  text  have  largely  been  un- 
shaded isometric  drawings  of  objects  used  in  the  class- 
room. 

Problem  i. — Make  an  isometric  drawing  of  a  chalk 
or  cigar  box  with  the  lid  open.  Scale,  half  size.  No 
dimensions. 

Problem  2. — Select  a  good-sized  spool.  Draw  in 
isometric.  Scale,  double  size.  No  dimensions. 

Problem  J. — Copy  the  exercise  of  the  connecting  rod, 
Fig.  127.  Scale,  full  size.  Dimension. 

Problem  4. — Figure  128  represents  the  base  and  cap 


MECHANICAL  DRAWING 


125 


of  a  pattern  for  a  pillow-block  bearing.  Scale,  full 
size.  Dimension. 

Problem  5. — The  teacher's  desk  to  suitable  scale. 
Do  not  show  invisible  lines.  Dimension.  Substitute 
a  book-case. 

Problem  6. — A  mission  chair.  Look  for  non-iso- 
metric lines.  Dimension,  and  draw  to  suitable  scale. 

Problem  /. — A  shaft-hanger.  Scale,  half  size.  Iso- 
metric. Fig.  129. 


Fie.  129 


CHAPTER  XI 

MISCELLANEOUS   EXERCISES 

Problem  I. — To  construct  the  arc  of  a  circle  me- 
chanically when  it  is  inconvenient  to  determine  its 
radius,  Fig.  130,  make  AB  the  chord  of  the  arc  ACB ; 
DC  and  ACB  to  be  kept  constant  and  the  position 
changed  so  that  points  A  and  B  remain  in  contact  with 
lines  AC  and  BC.  The  resultant  points  will  determine 
the  center  and  circumference  of  the  required  circle. 
The  same  problem  might  be  constructed  if  strips  be 
nailed  together  as  the  lines  AC  and  BC  suggest  with 
a  third  strip  crossing  lines  AC  and  BC  parallel  to  AB, 
anywhere,  to  hold  the  angle  firmly  thus  made. 

Problem  2. — A  graphical  method  for  finding  the 
distance  AB  across  a  pond  when  the  land  in  triangle 
FED  is  inaccessible.  Set  a  stake  at  C  in  line  with  AB 
prolonged.  Set  another,  D,  so  that  C  and  B  can  be 
seen  from  it.  Also  a  third  stake,  E,  in  line  with  BD 
prolonged  so  that  DE  equals  BD.  Set  a  fourth  stake, 
F,  at  the  intersection  of  EA  and  CD.  Measure  AC, 
AF  and  FE.  Show  that  AB  is  a  fourth  proportional 
to  AF,  AC  and  (FE— AF).  Draw  a  line  through  D 
parallel  to  AB.  D  bisects  BE.  DX  is  always  AB. 
Fig.  131.  2 

Problem  j. — Draw  an  involute  cam  which  involves 
the  construction  of  the  involute  curve  on  page  51. 

A  cam  is  a  very  useful  mechanical  device  which 
gives  various  motions  to  machine  parts  at  regular  in- 
tervals of  time.  It  is  generally  in  the  form  of  a  flat 


MECHANICAL  DRAWING 
C 


127 


Fig.  130 


disk,  although  sometimes  cylindrical  in  shape.  Har- 
vesters, printing  presses,  sewing  machines,  looms  and 
steam-valve  mechanisms  employ  a  considerable  use 


123 


A  PRACTICAL  COURSE  IN 


BANGLE  OF 
ACT/ ON 

Fie-  132 

of  cam  constructions,  Fig.  132.  To  draw  an  involute 
cam  with  a  given  rise  in  a  given  angle  of  action,  use 
the  following: 

Let  A  =  rise  of  the  follower  or  throw, 
And  X  =.  the  radius  of  the  base  circle  C. 
As  in  the  figure,  the  angle  of  action  is  120  degrees, 
A  =  %  X,  %  being  the  ratio  of  the  arc  through 


MECHANICAL  DRAWING 
<ry 
OJ 


129 


which  the  cam  works,  to  a  semicircle  or  straight  angle. 

2,  =.  44/21  X,  assuming  -n-  to  be  3  1/7. 

X,  or  the  radius,  =  2/44/21  =  2x21/44  =  42/44 
in.,  or  nearly  i". 


130  A  PRACTICAL  COURSE  IN 

We  assume  ^f  as  being  most  convenient.  With  this 
radius  draw  the  base  circle  C,  and  construct  tangents 
upon  which  to  lay  out  the  involute  curve.  The  ma- 
chine itself  will  determine  the  diameter  of  the  disk. 
Lay  off  the  rise  of  the  follower  on  tangent  i,  and  di- 
vide this  into  as  many  parts  as  tangents  have  been 
constructed.  With  center  O,  draw  concentric  circles 
to  corresponding  tangents  from  the  points  on  the  axis 
of  the  follower  (F). 

THE    HELIX 

Problem  4. — Fig.  133  shows  the  development  of  a 
helical  curve  as  unwrapped  from  a  cylinder.  If  the 
surface  of  the  cylinder  be  laid  out  on  paper  and  a 
diagonal  line  be  drawn  and  the  paper  wrapped  about 
the  cylinder,  the  line  will  then  illustrate  the  helix. 

Problem  5. — The  application  of  the  helix  may  also 
be  seen  in  coil  springs,  two  illustrations  of  which  are 
given.  Fig.  134.  The  constructions  may  be  laid  out 
as  in  Fig.  50,  page  52.  As  in  a  screw  thread  the  pitch 
of  the  helix  is  the  distance  between  two  opposite 
points  lying  on  the 'curve  and  the  same  cylindrical  ele- 
ment. In  drawing  the  spring,  use  the  helical  curve  as 
a  centerline.  Draw  a  number  of  srnall  circles  equal 
to  the  diameter  of  the  round  coil  desired.  The  con- 
tour may  easily  be  defined  by  drawing  tangent  helices 
to  these  circles.  If  square  or  rectangular  material  is 
used,  draw  the  helices  from  each  of  the  four  corners, 
A,  B,  C,  D,  of  the  cross  section. 

Problem  6. — Make  a  coil  spring  from  5"  round 
steel,  3^/2"  inside  diameter,  1^/2"  pitch  and  6"  long. 

Problem  7. — Make  also  a  square  spring  out  of  half- 
inch  material,  1^4"  pitch,  4"  outside  diameter  and 
6"  length. 


MECHANICAL  DRAWING 


131 


Problem  8. — Determine  the  length  of  material  re- 
quired in  each  preceding  problem. 


c D 


SHEET-METAL  PROBLEMS 

On  page  91  references  were  made  to  the  value  of 
knowing  how  to  lay  out  a  pattern  or  template  for  sheet- 
metal  problems.  To  the  sheet-metal  draftsman  more 
particularly  than  any  other  the  use  of  geometric 
methods  in  drafting  is  most  practical. 

A  great  many  problems  of  a  sheet-metal  character 
are,  at  least,  in  part  warped  surfaces.  Such  surfaces 
are  non-developable  by  any  regular  method.  In  the 
development  of  Fig.  97,  the  cone  is  first  divided  into 
elements  of  regular  intervals,  say  12  in  all,  and  their 
true  length  determined  by  revolving  each  fore- 
shortened element  parallel  to  the  vertical  view.  Any 
two  true  elements  laid  out  with  the  chord  of  their 
basal  arc  will  form  a  triangle.  Adjacent  triangles  are 


132  A  PRACTICAL  COURSE  IN 

constructed  in  a  similar  manner  and  the  pattern  com- 
pleted. 

Problem  p. — Fig.  135  is  an  illustration  of  a  tran- 
sition piece  for  a  smokestack  or  blower.  Draw  to  scale 
of  i"  equals  I'-o".  Fig.  136  shows  the  pattern  when 
laid  out. 

By  observation  it  will  be  seen  that  planes  A,  B,  C,  D, 
are  triangles  whose  true  shapes  can  easily  be  deter- 
mined from  the  projections.  The  four  corners  are 
sections  of  oblique  cones  which  have  been  previously 
described.  But  a  shorter  method  of  finding  the  true 
length  of  these  elements  is  to  find  the  hypotenuse  of 
a  right  angle  the  base  of  which  is  the  distance  from 
X  or  Y  in  the  plan,  to  points  3,  4,  5  and  6  in  the  plan. 
The  altitude  of  each  triangle  is  the  projected  vertical 
altitude  as  seen  in  the  front  view.  Lay  off  the  side; 
anywhere  as  at  OP  and  draw  each  hypotenuse.  These 
are  the  true  lengths  desired  in  the  pattern  between 
planes  A,  B,  and  C.  The  true  lengths  of  other  ele- 
ments are  found  in  a  similar  way.  As  the  section  of 
the  top  is  a  circle  taken  at  an  angle  of  30  deg.  from  a 
horizontal,  an  auxiliary  view  will  show  a  true  circle  as 
in  the  front,  or  top  view.  A  semicircle  will  suffice. 
Divide  into  an  equal  number  of  points  for  convenience 
and  project  back  to  the  corresponding  plan  and  eleva- 
tion. Connect  these  points  with  R,  X,  Y  and  Z,  and 
proceed  with  the  development. 

Lay  off  plane  A  first.  Fig.  136.  With  6  as  a  cen- 
ter, strike  an  arc  equal  to  6 — 5  (on  the  section)  and 
the  pattern  with  Y  as  a  center  and  a  radius  equal  to 
5 — 5  at  OP.  Continue  this  process  until  each  of  the 
longer  diagonals  are  used,  half  on  each  side  of  plane 


MECHANICAL  DRAWING 


Fig.  135 


134 


A  PRACTICAL  COURSE  IN 


A.  When  all  of  the  longer  diagonals  are  used  add 
planes  B  and  C,  and  then  add  the  diagonals  laid  out 
on  the  left  of  OP.  The  plane  D  is  bisected  to  show 
a  symmetrical  development. 


Fig.  136 


Problem  10. — Fig.  137  is  the  layout  and  working 
drawing  of  the  base  of  a  smokestack.  The  top  of 
the  base  is  circular  in  shape  while  the  ends  are  semi- 
oblique  cones.  Make  a  development  of  y2  the 
lateral  surface  similar  in  shape  to  Fig.  136,  scale  i" 
equals  I'-o". 

In  this  problem  it  will  be  necessary  to  find  the  true 
length  of  all  elements  by  revolving  the  true  length  (of 
all)  parallel  to  the  vertical  plane  upon  which  the  front 
view  is  projected.  To  do  this  use  X'  as  a  center  and 


MECHANICAL  DRAWING 


135 


X' — 6  as  a  radius.  Strike  an  arc  upon  0 — X'.  Project 
up  to  the  plane  AB.  Connect  the  newly  found  point 
with  X  and  the  line  will  now  be  seen  in  its  true  length 
as  it  is  parallel  to  V. 


Fig.  137 

When  the  plane  CD  cuts  the  new  position,  X' — 6 
will  be  the  true  length  of  that  portion  which  consti- 
tutes the  surface  and  can  be  laid  off  on  X" — 6  of  the 
development.  Fig.  138. 


136 


A  PRACTICAL  COURSE  IN 


\ 

'£  HALF  OF  DEVELOPMENT^ 


Fig.  138 

Problem  n. — Fig.  139  is  an  illustration  of  a  gro- 
cer's scale  scoop. 

The  development  of  A  is  a  pattern  of  the  portion 
of  a  cylinder  which  a  tinsmith  would  be  required  to' 
lay  out  for  a  template.  Substitute  suitable  dimensions 
and  draw.  Draw  a  center  line  X-X  to  begin.  Divide 
the  end  view  of  section  A  into  a  convenient  number  of 
similar  (equal)  parts.  Project  back  to  X-X.  The 
circumference  of  section  A  is  next  laid  out  in  de- 


MECHANICAL  DRAWING 


137 


Fig.  139 

velopment  anywhere  convenient  and  the   points  pro- 
jected to  corresponding  places. 

SECTIONS  OF   WORKING  DRAWING 

The  value  of  being  able  to  make  sections  in  a  draw- 
ing where  possible  constructive  difficulties  may  arise 
later,  is  a  part  of  the  draftsman's  business.  Sections 
are  very  helpful  in  showing  interior  constructions  and 
in  a  complicated  drawing  are  absolutely  necessary. 
In  the  illustrations,  the  sections  are  shown  by  cross 
hatching  lines,  the  relation  of  adjacent  parts  being 


138 


A  PRACTICAL  COURSE  IN 


Fie.  140 


shown  by  drawing  the  hatch  lines  at  different  angles. 
To  determine  the  location  of  sections,  pass  planes 
through  the  geometric  centers  of  the  object,  both  ver- 
tical and  horizontal.  On  pages  92  and  93  and  else- 
where of  chapter  VIII,  sections  were  made  of  geomet- 
ric solids  and  their  developments  required.  Figs.  140 
and  141  are  sections  of  small  machine  parts  and  illus- 


MECHANICAL  DRAWING 


139 


Fig.    42 

trate  the  practical  value  of  such  a  construction.  Fig. 
142  is  a  sole  plate  for  a  pillow  block.  Make  freehand 
sketches  of  each  of  the  sectioned  illustrations  in  order 
to  get  a  pictorial  view  of  the  object. 

Problem  12. — On  page  67  is  an  illustration  of  a 
core  box  for  a  pipe  tee. 

Fig.  143  is  an  isometric  illustration  of  a  pipe-tee 


Fig.  143 


140 


A  PRACTICAL  COURSE  IN 


pattern  but  not  for  the  box  just  referred  to.     Make 
three  views  from  the  illustration,  full  size. 

Problem  /j. — Fig.  144  is  an  illustration  of  a  pat- 
tern for  a  pedestal  bearing.     Make  three  views,  9"  = 

I'-O". 


Fig.  144 


Problem  14. — Fig.  145  is  an  assembly  drawing  of 
a  simple  machine  vise.  Make  a  detail  drawing  filling 
all  blank  dimensions  as  indicated  in  Figs.  146  and  147. 
Those  dimensions  which  are  apparently  omitted  should 


MECHANICAL  DRAWING 


141 


Fig.  I4S 


142 


A  PRACTICAL  COURSE  IN 


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MECHANICAL  DRAWING                      143 

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144  A  PRACTICAL  COURSE  IN 

be  supplied  by  the  student;  but  reference  should  be 
made  to  the  assembly  drawing  before  so  doing.  Make 
a  full-size  drawing  of  the  assembled  vise  before  the 
detail  drawing.  Make  a  stock  list  as  suggested  on 
page  86.  Notes  on  the  detail  drawing  have  reference 
to  the  work  of  the  machinist  in  "finishing"  the  cast- 
ing after  it  has  been  molded  from  the  pattern.  Such 
information  is  essential  to  a  workman  and  eliminates 
hazardous  guesses  and  mistakes  as  well  as  loss  of 
time  and  material.  The  arrangement  of  pieces  and 
parts  should  be  very  carefully  planned  on  the  drawing 
paper.  In  so  doing  much  more  can  be  placed  on  one 
sheet  Look  for  necessary  alterations  on  your  drawing. 

Problem  15. — Figs.  148  and  149  represent  a  small 
jack  screw  in  section  and  detail.  Make  three  views 
and  dimension. 

Problem  16. — Fig.  150  is  an  illustration  of  Hooke's 
coupling.  Three  views  and  section. 

Problem  //. — Fig.  151  is  a  side  crank  arm.  Make 
three  views  and  section  at  X-x. 

Problem  18. — Fig.  141,  page  138,  is  a  turnbuckle. 
Make  three  views  and  section. 

Make  a  drawing  of  each  problem  above  to  scale  as 
suggested.  Use  suitable  diameters  in  each  case  and 
section. 

Problem  ig. — Make  an  isometric  drawing  of  the 
mission  footstool  as  shown  in  Fig.  152. 

INTERSECTIONS    AND    PENETRATIONS 

Problem  20. — The  three  views  of  a  stub  end  of  a 
connecting  rod  are  shown  in  Fig.  153.  To  find  the 
curve  of  intersection,  of  the  cone  and  prism,  pass 
vertical  planes  A,  B,  C,  D,  cutting  both  the  cone  and 
rectangular  prism.  Each  plane  cuts  a  circle  from  the 
cone  and  a  rectangle  from  the  prism.  Where  these 


MECHANICAL  DRAWING 


145 


3/6   ^ H \/6 


Fig- 148 


146 


A  PRACTICAL  COURSE  IN 


Fig.  149 


figures  intersect  is  a  point  of  the  curve  desired.    The 
same  method  is  used  in  finding  a  curve  of  intersection 


MECHANICAL  DRAWING 


147 


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Fig.  151 


148 


A  PRACTICAL  COURSE  IN 


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Fig.  152 


of  a  cone  and  hexagonal  prism,  or  the  chamfered  por* 
tion  of  a  hexagonal  nut. 


MECHANICAL  DRAWING 


149 


Fig.  153 


150  A  PRACTICAL  COURSE  IN 

LETTERING   EXERCISES 

A  great  deal  of  the  difficulty  which  comes  to  the 
beginner  in  lettering  is  due  to  a  vague  idea  of  the 
shape  of  the  individual  letter.  No  draftsman,  however 
experienced,  can  produce  well  formed  letters  without 
a  clear  picture  of  the  shape  of  each  letter  and  for  this 
reason  the  beginning  student  should  read  and  follow 
these  suggestions  closely.  Use  practice  paper,  before 
commencing  one  of  the  exercises  below. 

INSTRUCTIONS 

1.  Make  the  vertical  stroke  of  A,  first,  then  the 
slanting  stroke. 

2.  Make   the  bottom   part  of   B   wider   than   the 
upper. 

3.  Letters  C,  G  and  Q  are  modifications  of  the 
letter  O. 

4.  Keep  the  bottom  part  of  the  letter  D  full. 

5.  The  lowest  bar  of  the  letter  E  is  a  little  longer 
than  the  upper  bar.     The  middle  bar  is  shortest  and 
slightly  above  the  center  as  in  F. 

6.  Draw  the  two  outside  bars  of  the  letter  H  first. 
Horizontal  bar  is  slightly  above  center. 

7.  The  letter  J  is  a  portion  of  the  letter  U. 

8.  Make  the  short  bar  of  the  letter  K  slope  from 
the  upper  end  of  the  first  bar. 

9.  Letter  M  is  broad.     Draw  the  two  outside  bars 
parallel,  first,  before  the  intermediate,  likewise  in  the 
letter  N. 

10.  Letters  P  and  R  are  similar.     Keep  the  top 
full. 

n.  The  letter  S  may  best  be  made  inside  the  letter 
O,  with  the  bottom  part  a  little  wider  and  fuller. 


ALL  LETTERS  SLOPE  HALF  THE  H/GHT 

/   3^5        3.^ 


CARL  SCHURZ  HIGH 
SCHOOL 

ABCDEFGHIUKLMNOPQR 
STUVWXYZ 


THE  QUICK  BROWN  FOX  JUMPS 
OVER  THE* LAZY  DOG. 

Fie.  154 


152 


PENCIL    EACH  LETTERING   SHEET  ON 
CROSS    SECTION  PAPER  PROVIDED    FOR    THAT 
PURPOSE  AND   SUBMIT  EACH  PENCILLED 
L/NE    TO    THE  INSTRUCTOR   f=~QR  HIS 
CR/T/C/SM.        /N  DOING    THIS    THE  STUDENT 
WILL.   SAVE     T/ME  AND   IMPROVE    HIS 
STANDARD    OF    WORKMANSHIP  MORE  FfAP/DLY. 

USE  A    <2/y  PENCIL    CON/CAL    ROINT.        ALL 
DPAW/NGS  SHOULD  BE  KEPT  NEAT  AND 
CLEAN.      SPACES   BETWEEN    WORDS   SHALL 
NOT    VARY  FROM  LESS    THAN  S    TO  MORE 
THAN  3  DIV/SIONS    ON    THE    CROSS    SECT/ON 
&ARER.        SPACES    BETWEEN  PARAGRAPHS 
SHOULD   BE  DOUBLE    THE    SPACE  BETWEEN 
LINES.         A  SINGLE    SPACE  /S    SUFFICIENT 
TO   SEPARATE   LINES   IN    THE    PARAGRAPH. 

INDENT  EACH  NEW  PAPAGPfAPH.         USE  A 
LARGE  PEN* HOLDER.     WITH   A   SIG    EF"   PEN 
PO/NT.       KEEP    THE  PENPOINT   CLEAN   TO 
ALLOW   A   STEADY  FLOW    OF  INK.         THE  INK 
CLOGS    THE  REN^S   ACTION  VERY    QUICKLY. 
DO  NOT  FILL     THE  REN  FULL     OF   INK    IF    YOU 
W/SH    TO  DO   EVEN  LETTERING    AND   AVOID 
BLOT&. 

IN  DEN  T 


REPEAT    LAST    RARAGRARH 


Fie    155 


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Fie.  157 


MECHANICAL  DRAWING  155 

12.  Make  the  first  bar  of  the  W  slope  slightly  to 
the  right.     Keep  the  letter  broad. 

13.  Letter  V  is  the  letter  A  upside  down. 

14.  Widths  of  all  letters  are  in  proportion  to  their 
heights  and  should  be  always  so  considered. 

15.  Common  practice   among  draftsmen   employs 
the  use  of  the  sloping  Gothic  letter.     Vertical  letters 
are  commonly  used,  however,  but  are  more  tedious  to 
make  look  well. 

Problem  21. — Make  an  exercise  on  %-in.  coordi- 
nate paper  of  Fig.  154. 

Each  small  figure  pertains  to  the  number  of  spaces 
upon  the  section  paper.  This  exercise  is  a  study  in 
form  and  proportion  and  should  be  executed  with 
much  precision  and  care.  Use  2-H  pencil,  conical 
point. 

Problem  22. — Fig.  155  is  an  exercise  in  lettering 
one  space  high.  Herein  is  the  application  of  the  exer- 
cise in  Fig.  154. 

Problem  23. — Read  the  material  over  carefully  and 
apply  the  directions  included  therein.  Hard  practice 
is  a  good  master.  Fig.  156  is  an  exercise  of  figures 
and  fractions  on  cross-section  paper.  The  draftsman's 
figures  are  quite  different  from  the  commercial  figure 
and  hence  should  be  scrutinized  closely.  Fill  in  all 
vacant  spaces  and  strive  for  uniformity  as  in  previous 
exercises. 

Problem  24.  — Fig.  157  is  an  exercise  in  block  let- 
tering quite  often  used  in  designs  for  covers,  titles, 
headings,  etc.  Note  the  divisions  of  the  height  are  5 
instead  of  8. 


CHAPTER  XII 

A   SUGGESTED   COURSE   FOR    HIGH    SCHOOLS 

Group  i.     Geometric  Exercises 

Problem  i. — Bisect  a  given  right  line  and  arc. 

Problem  2. — Erect  _Ls  to  a  given  line  (any  method). 

Problem  j. — Draw  parallel  lines  (two  methods). 

Problem  4. — Divide  a  given  line  into  proportional 
parts. 

Problem  5. — Construct  tangents  to  a  given  arc  of  any 
radius.  (Fillet.) 

Problem  6. — Duplicate  and  bisect  a  given  angle. 

Problem  7. — Without  triangles  construct  A  of  30", 
60°,  75°,  45°.  220-30',  37°-3°'- 

Problem  8. — By  triangles  only  divide  a  semicircle 
into  angles  of  15°. 

Problem  9. — Rectify  a  quadrant  of  a  circle  (two 
methods).  Approximate. 

Problem  10. — Triangles   (trilium — trefoil). 

a.  Right  angle  (rise,  run  and  pitch  of  a  gable  roof 
rafter)  x2+y2  =  z2. 

To  find  the  distance  across  an  unknown  area — a 
stream,  lake  or  park ;  also  to  find  altitude  of  a  tree. 

b.  Equilateral.     (Isometric  square — Gothic  arch). 

c.  Isosceles. 

d.  Scalene. 

Query:     How  find  the  area  of  any  triangle? 
What  is  the  sum  of  all  angles  of  a  triangle? 
Problem    n.     Square    (bolthead    plan — swastika — 
syringa). 


MECHANICAL  DRAWING  157 

Problem  /<?.— Polygons  (pansy,  violet — crystals). 

a.  Pentagon — star  (three  methods). 

b.  Hexagon — bolthead  plan  (two  methods) — star. 

c.  Heptagon. 

d.  Octagon — taboret  top. 

e.  Combination  of  a,  b,  c,  d  on  a  given  side  of  i". 

211 — 4X90 
Prove  all  polygons  by  the  formula  —  —  when 

n 

n  =  the  number  of  sides  of  polygon.     Use  the  pro- 
tractor to  verify. 

Problem  /j — Circles  : 

a.  Three  circles  within  an  equilateral  triangle. 

b.  Draw   circles    tangent   to   each   other    and  the 
given  circle,  within  or  without. 

c.  Gothic  arch. 

d.  A  circle  tangent  to  a  given  circle  and  line. 

e.  A  circle  tangent  to  two  given  circles  which  are 
not  tangent  to  each  other.     Note :     The  smallest  circle 
is  not  acceptable. 

*/.  A  shaft  iy2"  in  diameter  rotates  within  a  ball- 
bearing consisting  of  twelve  tempered  steel  balls. 
Make  a  drawing  showing  size  of  balls  required. 

g.     Four  circles  within  a  square. 

h.     Maltese  cross. 

i.     Geometric  circular  borders. 

j.  Moldings — cavetto,  cyma,  reversa,  cyma  recta, 
ogee,  scotia. 

Problem  14. — Ellipses  and  elliptic  curves  (conic  sec- 
tions— ecliptic). 

a.  Focal  method ;  circle  method. 

b.  Trammel  method. 

r.     Five-point  elliptic  arch. 


158  A  PRACTICAL  COURSE  IN 

d.  Greek,  Persian  and  Gothic  arches. 

e.  Elliptic  cam. 

*/.  The  path  of  a  point  on  a  connecting  rod  in  one 
revolution. 

*</.  Cycloid.          ^| 

*h.  Epicycloid.      }•  ( Gear  teeth.) 

i.  Hypocycloid.  J 


*/.      Parabola. 


(Conic  sections.) 


*k.     Hyperbola. 
Problem  15. — Spirals : 

a.  Archimedean  spiral  of  one  or  more  whorls. 

b.  Ionic  volute  (Ionic  capital). 

*c.     Heart     plate     cam     (sewing-machine     bobbin- 
winder). 

*d.     Involute  (gear  teeth). 

*e  Helix-screw  thread,  clutch  coupling. 
Biographical. — From  the  encyclopedia  read  the  biog- 
raphies of  Archimedes,  Pythagoras,  Euclid,  Vignola. 
It  is  intended  that  the  number  of  problems  shoi'ld  be 
arranged  on  the  plate  according  to  the  local  conditions 
of  the  class-room.  Large  plates,  say  I5"x2o",  are 
more  comprehensive  but  require  less  time  for  execu- 
tion in  proportion  to  smaller  plates.  Such  problems  in 
this  outline  which  have  not  been  given  in  the  text  are 
not  essential,  but,  if  desired,  may  be  obtained  from  the 
instructor.  Those  who  expect  to  study  design  are  not 
required  to  complete  the  entire  course  of  mechanical 
drawing.  The  problems  marked  by  (*)  may  be 
omitted  in  this  group. 

Group  2.    Projections. 

I.     Working  drawings. 

1.  Three  views  of  a  cylinder. 

2.  Three  views  of  a  prism. 


MECHANICAL  DRAWING  159 

3.  Two  views  of  a  plinth — one  view  given, 

4.  Three  views  of  a  pyramid. 

5.  Hexagonal  nut. 

6.  Crank  arm. 

7.  Small  pedestal  bearing. 

8.  Taboret  or  stand. 

9.  Coat-hanger. 

10.  Knife-box. 

11.  Tailstock. 

12.  Tool-rest. 

Note :  The  first  eight  problems  are  not  to  be  di- 
mensioned. Substitutes  may  be  selected  for  these 
objects  where  and  when  these  are  not  available  or 
advisable.  Problems  8  to  15  are  to  be  dimensioned 
carefully.  Models  are  to  be  preferred  to  a  drawing  at 
the  beginning  of  this  course,  so  that  the  absolute  rela- 
tion of  object  to  drawing  will  be  established  as  early  as 
possible. 

13.  Detailed  working  drawings  from  machine  parts. 

14.  Working  drawings  from  isometric  blueprints. 

15.  Working  drawings  from  sketches  (freehand). 
//.     Revolution — Axes  of  symmetry. 

1.  Draw  three  views  of  a  prism,  plinth  or  pyramid. 

2.  Draw  three  views  of  No.  i  when  revolved  about 
a  vertical  axis  30°,  contra-clockwise. 

3.  From    No.    2    revolve   object   about    side   axis 
through  30°  to  the  left. 

4.  From  No.  I  revolve  the  object  forward  about  a 
front  axis  20°. 

5.  From  No.  2  revolve  the  object  backward  about  a 
front  axis  25°. 

6.  From  No.  5,  30°  about  a  side  axis,  to  the  right. 

7.  From  No.  4,  15°  about  a  vertical  axis. 

8.  From  No.  5,  15°  to  the  right  about  a  side  axis. 


160  MECHANICAL  DRAWING 

Several  plates  involving  the  modified  positions  of 
geometric  figures  should  be  drawn  that  the  theory  of 
projections  may  be  perfectly  clear.  Learn  the  three 
laws  of  revolution  given. 

///.     The  point,  line  and  plane.     (For  advanced  stu- 
dents.)    Draw  in  both  first  and  third  angles. 

1.  Find  H  and  V  projections  of  a  point  i1/^"  in 
front  of  V  and  2^/4"  above  H.     Two  inches  below  H 
and  il/2"  behind  V.     Always  open  the  first  angle. 

2.  Draw  the  projections  of  a  line  which  is  ff  to  the 
H  and  V  planes,  1^4"  above  H  and  2"  in  front  of  V. 

3.  Draw  two  views  of  a  line  oblique  to  H  and  // 
to  V ;  oblique  to  V  and  //  to  H  ;  oblique  to  H  and  V. 

4.  Find  the  true  length  of  lines  in  No.  3.     What  is 
the  difference  between  the  projected  length  and  the 
true  length  of  a  line  ? 

5.  Pass  a  plane  (a)  /  to  H;  (&)  //  to  V;  (c)  / 
to  P;  (d)  1  to  H,  and  any  /_  with  V;  (e)  1  to  (V) 
and  any  /_  with  H  and  P. 

6.  Find  the  intersection  of  a  and  b,  also  d  and  c  in  5. 
IV.     Development  of  surfaces  for  patterns  of  sheet- 
metal  and  tinsmithing. 

1.  Parallel  lines.     Cylinders,  prisms,  etc. 

2.  Radial  lines.     Cones,  pyramids,  etc. 

3.  Method  of  triangles.     Warped  surfaces. 

4.  Method  of  revolution.     Frustums  and  trunca- 
tions. 

5.  Method  of  parallel  planes ;  oblique  planes.     Pen- 
etrations. 

V .     Penetrations  with  developments  included. 
VI.     Shades  and  shadows. 
VII.     Mechanical   perspective. 


r 


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